A method and apparatus for performing hypothermia of a selected organ without significant effect on surrounding organs or other tissues. A flexible catheter is inserted through the vascular system of a patient to place the distal tip of the catheter in an artery feeding the selected organ. A compressed refrigerant is pumped through the catheter to an expansion element near the distal tip of the catheter, where the refrigerant vaporizes and expands to cool a flexible heat transfer element in the distal tip of the catheter. The heat transfer element cools the blood flowing through the artery, to cool the selected organ, distal to the tip of the catheter.