Abstract: A method and apparatus for performing hypothermia of a selected organ without significant effect on surrounding organs or other tissues, by perfusion of the organ with blood cooled externally from the body of the patient. A flexible supply catheter is inserted percutaneously into an artery. Blood from the supply catheter is cooled in a finned tube heat exchanger or a fluid bath. A flexible delivery catheter is inserted percutaneously through the vascular system of the patient to place the distal end of the catheter in an artery feeding the selected organ. An occlusion device is expanded to occlude the feeder artery at a point proximal to the distal end of the delivery catheter. Cooled blood from the chiller is pumped through the delivery catheter to an outlet near the distal end of the catheter, to cool the selected organ, distal to the tip of the delivery catheter.