PREFERRED STOCK WARRANT

Exhibit 10.15

PREFERRED STOCK WARRANT

NEITHER THIS WARRANT NOR THE SECURITIES ISSUABLE UPON EXERCISE OF THIS WARRANT HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. NO SALE OR DISPOSITION MAY BE EFFECTED EXCEPT IN COMPLIANCE WITH RULE 144 UNDER SAID ACT OR WITHOUT AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL FOR THE HOLDER, SATISFACTORY TO THE COMPANY, THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE ACT OR RECEIPT OF A NO-ACTION LETTER FROM THE SECURITIES AND EXCHANGE COMMISSION.

WARRANT TO PURCHASE SHARES OF SERIES F PREFERRED STOCK

Dated: May 31, 2005

THIS CERTIFIES THAT, for value received, Oxford Finance Corporation, (“Holder”) is entitled to subscribe for and purchase that number of shares as set forth in paragraph 1 below of the fully paid and non-assessable Series F Preferred Stock (the “Shares” or the “Preferred Stock”) of Alsius Corporation, a California corporation (the “Company”), at the Warrant Price (as hereinafter defined), subject to the provisions and upon the terms and conditions hereinafter set forth. As used herein, the term “Series F Preferred Stock” shall mean the Company’s presently authorized Series F Preferred Stock, and any stock into which such Series F Preferred Stock may hereafter be exchanged.

1. Warrant Price. The Warrant Price shall initially be the lower of (i) Three Dollars ($3.00) per share and (ii) the lowest effective price per share (on a common stock equivalent basis and taking into account any securities issued together with the preferred stock) at which shares of the Company’s convertible preferred stock are sold in the next Qualified Financing; provided, however, if the Qualified Financing has not closed prior to the exercise of this Warrant, then the Warrant Price shall be Three Dollars ($3,00) per share. A “Qualified Financing” shall mean the sale of the convertible preferred stock of the Company to purchasers which include venture capital investors in an aggregate gross cash amount not less than $2,000,000 (excluding any bridge debt actually converted into equity.). The number of shares for which this Warrant is exercisable shall be the nearest whole number determined by dividing $350,000 by the Warrant Price determined pursuant to this paragraph

2. Conditions to Exercise. The purchase right represented by this Warrant may be exercised at any time, or from time to time, in whole or in part during the term commencing on the date hereof and ending on the earlier of:

In the event that, although the Company shall have given notice of a transaction pursuant to subparagraph [3(e)] hereof, the transaction does not close within 60 days of the day specified by the Company, unless otherwise elected by the Holder any exercise of the Warrant subsequent to the giving of such notice shall be rescinded and the Warrant shall again be exercisable until terminated in accordance with this Paragraph 2.

3. Method of Exercise; Payment; Issuance of Shares; Issuance of New Warrant.

Where X = the number of shares of Series F Preferred Stock to be issued to Holder.

Y = the number of shares of Series F Preferred Stock purchasable under this Warrant (at the date of such calculation).

A = the Fair Market Value of one share of the Company’s Series F Preferred Stock (at the date of such calculation).

B = Warrant Exercise Price (as adjusted to the date of such calculation).

In the event of 3(c)(ii) or 3(c)(iii), above, the Company’s Board of Directors shall prepare a certificate, to be signed by an authorized Officer of the Company, setting forth in reasonable detail the basis for and method of determination of the per share Fair Market Value of the Series Preferred Stock. The Board will also certify to the Holder that this per share Fair Market Value will be applicable to all holders of the Company’s Series F Preferred Stock. Such certification must be made to Holder at least fifteen (15) business days prior to the proposed effective date of the merger, consolidation, sale, or other triggering event as defined in 3(c)(ii) and 3(c)(iii).

4. Representations and Warranties of Holder and Restrictions on Transfer Imposed by the Securities Act of 1933.

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE TRANSFERRED UNLESS COVERED BY AN EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT, A “NO ACTION” LETTER FROM THE SECURITIES AND EXCHANGE COMMISSION WITH RESPECT TO SUCH TRANSFER, A TRANSFER MEETING THE REQUIREMENTS OF RULE 144 OF THE SECURITIES AND EXCHANGE COMMISSION, OR (IF REASONABLY REQUIRED BY THE COMPANY) AN OPINION OF COUNSEL SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY SUCH TRANSFER IS EXEMPT FROM SUCH REGISTRATION.

The Company need not enter into its stock register a transfer of Securities unless the conditions specified in the foregoing legend are satisfied. The Company may also instruct its transfer agent not to register the transfer of any of the Shares unless the conditions specified in the foregoing legend are satisfied.

5. Condition of Transfer or Exercise of Warrant. It shall be a condition to any transfer or exercise of this Warrant that at the time of such transfer or exercise, the Holder shall provide the Company with a representation in writing that the Holder or transferee is acquiring this Warrant and the shares of Series

F Preferred Stock to be issued upon exercise, for investment purposes only and not with a view to any sale or distribution,, or will provide the Company with a statement of pertinent facts covering any proposed distribution and a written agreement that such Holder or transferee agrees to be bound by the provisions of this Warrant. As a further condition to any transfer of this Warrant or any or all of the shares of Series F Preferred Stock issuable upon exercise of this Warrant, other than a transfer registered under the Act, the Company must have received a legal opinion, in form and substance satisfactory to the Company and its counsel, reciting the pertinent circumstances surrounding the proposed transfer and stating that such transfer is exempt from the registration and prospectus delivery requirements of the Act. Each certificate evidencing the shares issued upon exercise of the Warrant or upon any transfer of the shares (other than a transfer registered under the Act or any subsequent transfer of shares so registered) shall, at the Company’s option, contain a legend in form and substance satisfactory to the Company and its counsel, restricting the transfer of the shares to sales or other dispositions exempt from the requirements of the Act.

As further condition to each transfer, the Holder shall surrender this Warrant to the Company and the transferee shall receive and accept a Warrant, of like tenor and date, executed by the Company.

6. Stock Fully Paid; Reservation of Shares. All Shares which may be issued upon the exercise of the rights represented by this Warrant will, upon issuance, be fully paid and non-assessable, and free from all taxes, liens, and charges with respect to the issue thereof. During the period within which the rights represented by this Warrant may be exercised, the Company will at all times have authorized, and reserved for issuance upon exercise of the purchase rights evidenced by this Warrant, a sufficient number of shares of its Series F Preferred Stock to provide for the exercise of the rights represented by this Warrant.

7. (a) Adjustment for Certain Events. In the event of changes in the outstanding Series F Preferred Stock by reason of stock dividends, split-ups, recapitalizations, reclassifications, mergers, consolidations, combinations or exchanges of shares, separations, reorganizations, liquidations, or the like, the number and class of shares available under the Warrant in the aggregate and the Warrant Price shall be correspondingly adjusted, as appropriate, by the Board of Directors of the Company. The adjustment shall be such as will give the Holder of this Warrant upon exercise for the same aggregate Warrant Price the total number, class and kind of shares as it would have owned had the Warrant been exercised prior to the event and had it continued to hold such shares until after the event requiring adjustment.

(b) Other Anti-dilution Protections. Additional anti-dilution rights applicable to the Series F Preferred Stock purchasable hereunder are as set forth in the Certificate of Incorporation. Such anti-dilution rights shall not be restated, amended, modified or waived in any manner that is adverse to the Holder hereof and different from other holders of Series F Preferred Stock without the Holder’s written consent. The Company shall promptly provide the Holder with any restatement, amendment, modification or waiver of the Certification of Incorporation.

8. Notice of Adjustments. Whenever any Warrant Price shall be adjusted pursuant to Section 7 hereof, the Company shall prepare a certificate signed by its president or chief financial officer setting forth, in reasonable detail, the event requiring the adjustment, the amount of the adjustment, the method by which such adjustment was calculated, and the Warrant Price and number of shares issuable upon exercise of the Warrant after giving effect to such adjustment, and shall cause copies of such certificate to be mailed (by certified or registered mail, return receipt required, postage prepaid) within thirty (30) days of such adjustment to the Holder of this Warrant as set forth in Section 19 hereof.

9. “Market Stand-Off” Agreement. Holder hereby agrees that for a period of up to 180 days following the effective date of the first registration statement of the Company covering common stock (or other securities) to be sold on its behalf of the Company in an underwritten public offering, it will not, to the extent requested by the Company and any underwriter, sell or otherwise transfer or dispose of (other than to designees or transferees who agree to be similarly bound) any of the Shares at any time during such period except common stock included in such registration; provided, however, that all officers and directors of the Company who hold securities of the Company or all other persons who own at least one percent (1%) of the Company’s outstanding voting equity securities enter into similar agreements.

10. Transferability of Warrant. This Warrant is transferable on the books of the Company at its principal office by the registered Holder hereof upon surrender of this Warrant properly endorsed, subject to compliance with Section 5 and applicable federal and state securities laws. The Company shall issue and deliver to the transferee a new Warrant representing the Warrant so transferred. Upon any partial transfer, the Company will issue and deliver to Holder a new Warrant with respect to the Warrant not so transferred. Holder shall not have any right to transfer any portion of this Warrant to any direct competitor of the Company.

11. Registration Rights. The Holder shall have piggyback registration rights.

12. No Fractional Shares. No fractional share of Series F Preferred Stock will be issued in connection with any exercise hereunder, but in lieu of such fractional share the Company shall make a cash payment therefor upon the basis of the Warrant Price then in effect.

13. Charges, Taxes and Expenses. Issuance of certificates for shares of Series F Preferred Stock upon the exercise of this Warrant shall be made without charge to the Holder for any United States or state of the United States documentary stamp tax or other incidental expense with respect to the issuance of such certificate, all of which taxes and expenses shall be paid by the Company, and such certificates shall be issued in the name of the Holder.

14. No Shareholder Rights Until Exercise. This Warrant does not entitle the Holder hereof to any voting rights or other rights as a shareholder of the Company prior to the exercise hereof.

15. Registry of Warrant. The Company shall maintain a registry showing the name and address of the registered Holder of this Warrant. This Warrant may be surrendered for exchange or exercise, in accordance with its terms, at such office or agency of the Company, and the Company and Holder shall be entitled to rely in all respects, prior to written notice to the contrary, upon such registry.

16. Loss, Theft, Destruction or Mutilation of Warrant. Upon receipt by the Company of evidence reasonably satisfactory to it of the loss, theft, destruction or mutilation of this Warrant, and, in the case of loss, theft, or destruction, of indemnity reasonably satisfactory to it, and, if mutilated, upon surrender and cancellation of this Warrant, the Company will execute and deliver a new Warrant, having terms and conditions substantially identical to this Warrant, in lieu hereof.

17. Miscellaneous.

18. No Impairment. The Company shall not by any action including, without limitation, amending its Sections or articles of incorporation or by-laws, any reorganization, transfer of assets, consolidation, merger, share exchange dissolution, issue or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of the Warrants or impair the ability of the Holder(s) to realize upon the intended economic value hereof, but will at all times in good faith assist in the carrying out of all such terms and in the taking of all such action as may be necessary or appropriate to protect the rights of the Holder(s) hereof against impairment. Without limiting the generality of the foregoing, the Company will (a) not increase the par value of any shares of Series F Preferred Stock issuable upon the exercise of the Warrants above the amount payable therefor upon such exercise, (b) take all such action as may be necessary or appropriate in order that the Company may validly issue fully paid and non-assessable shares of Series F Preferred Stock upon the exercise of the Warrants, (c) obtain all such authorizations, exemptions or consents from any public regulatory body having jurisdiction thereof as may be necessary to enable the Company to perform its obligations under the Warrants and (d) not reclassify or convert common stock and (f) not take or permit to be taken any action which would have the effect of shortening the period provided herein for exercise of the Warrants.

19. Addresses. Any notice required or permitted hereunder shall be in writing and shall be mailed by overnight courier, registered or certified mail, return receipt required, and postage pre-paid, or otherwise delivered by hand or by messenger, addressed as set forth below, or at such other address as the Company or the Holder hereof shall have furnished to the other party.

IN WITNESS WHEREOF,Alsius Corporation has caused this Warrant to be executed by its officers thereunto duly authorized.

Dated as of May 31, 2005.

NOTICE OF EXERCISE

1. The undersigned Warrantholder (“Holder”) elects to acquire shares of the Series F Preferred Stock (the “Preferred Stock”) of Alsius Corporation, (the “Company”), pursuant to the terms of the Stock Purchase Warrant dated May 31, 2005, (the “Warrant”).

2. The Holder exercises its rights under the Warrant as set forth below:

3. The Holder surrenders the Warrant with this Notice of Exercise.

4. The Holder represents that it is acquiring the aforesaid shares of Series F Preferred Stock for investment and not with a view to, or for resale in connection with, distribution and that the Holder has no present intention of distributing or reselling the shares.

Holder acknowledges and agrees to be bound by the provisions of the Warrant, including, without limitation, the Market Stand-off Agreement contained therein.

5. Please issue a certificate representing the shares of the Series F Preferred Stock in the name of the Holder or in such other name as is specified below: