AMENDMENT NO. 3 TO TENTH AMENDED AND RESTATED

Exhibit 10.13

AMENDMENT NO. 3 TO

TENTH AMENDED AND RESTATED

INVESTOR RIGHTS AGREEMENT

THIS AMENDMENT NO. 3 TO TENTH AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT (this “Amendment”), entered into on October 2, 2006, among ALSIUS CORPORATION, a California corporation (the “Company”), and the undersigned investors in the Company (the “Investors”).

RECITALS:

A. Certain of the Investors hold shares of the Company’s Common Stock, Series A, Series B, Series C-D, Series E and/or Series F Preferred Stock and possess registration rights, information rights, rights of first refusal, and other rights pursuant to that certain Tenth Amended and Restated Investor Rights Agreement, dated as of September 2, 2004, among the Company, such Investors and certain other shareholders of the Company (the “Original Agreement”).

B. The Tenth Restated Agreement was amended on April 13, 2006 (the “First Amendment”) and on August 18, 2006 (the “Second Amendment” and together with the Original Agreement and the First Amendment, the “Tenth Restated Agreement”)

C. On or about the date hereof, in connection with a bridge financing (the “Bridge Financing”), the Company is issuing a series of 8% Unsecured Convertible Promissory Notes (the “Bridge Notes”) and warrants to purchase Common Stock of the Company (the “Warrants”).

D. It is a condition to the closing of the Bridge Financing that this Amendment be executed by the parties hereto, and the parties are willing to execute, and to be bound by the provisions of, this Amendment.

E. The undersigned Investors desire to amend the definitions of “2006 Bridge Notes” and “Warrants” under Section 1.1 of the Tenth Restated Agreement to include the shares of stock issuable upon conversion of the Bridge Notes and exercise of the Warrants.

F. The Investors executing this Amendment hold a majority of the shares held by all Investors who are a party to the Tenth Restated Agreement and sixty percent (60%) of the shares of Series C-D, Series E and Series F Preferred Stock or Common Stock issuable upon conversion thereof, and therefore have the power under Section 3.6 of the Tenth Restated Agreement to amend such agreement.

NOW, THEREFORE, in consideration of the mutual promises and covenants set forth herein, the parties to the Tenth Restated Agreement hereby agree that the Tenth Restated Agreement shall be amended as follows:

1. Revised Definition of 2006 Bridge Notes in Section 1.1. The undersigned Investors hereby agree that the definition of 2006 Bridge Notes, which was added to Section 1.1 of

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the Original Agreement by the First Amendment and amended by the Second Amendment, shall be deleted in its entirety and replaced with the following:

“2006 Bridge Notes” means the convertible promissory notes made by the Company, dated April 13, 2006, August 18, 2006, October 2, 2006 and such other dates as promissory notes may be made by the Company in connection with bridge financings of the Company of approximately $8,700,000 or such increased amount as unanimously approved by the Board of Directors.”

2. Revised Definition of “Warrants in Section 1.1.” The undersigned Investors hereby agree that the definition of “Warrants” in Section 1.1 of the Tenth Restated Agreement shall be deleted in its entirety and replaced with the following:

““Warrants” means those certain warrants to purchase Common Stock of the Company (i) dated April 30, 2003, issued to the initial purchasers of the Bridge Notes and (ii) dated April 13, 2006, August 18, 2006, October 2, 2006 and such other dates on which warrants may be issued to the initial purchasers of the 2006 Bridge Notes.”

3. Remainder of Tenth Restated Agreement Unchanged. Except as amended by this Amendment, the Tenth Restated Agreement shall otherwise remain in full force and effect.

4. Governing Law. This Amendment shall be governed by and construed under the laws of the State of California, without regard to its conflicts of laws provisions.

5. Counterparts. This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

6. Facsimile Signatures. This Amendment may be executed and delivered by facsimile and upon such delivery, the facsimile signature will be deemed to have the same effect as if the original signature had been delivered to the other parties. The original signature copy shall be delivered to the other parties by mail. The failure to deliver the original signature copy and/or the non-receipt of the original signature copy shall have no effect upon the binding and enforceable nature of this Amendment.

IN WITNESS WHEREOF, the undersigned Investors and the Company have executed this Amendment as of the day and year first above written.

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