Devices and methods for warming or cooling blood flowing through the vasculatureof a human or animal subject so as to alter or control the temperature of all or partof the subject's body. Heat exchangers are positioned within the subject'svasculature and heated or cooled heat exchange fluid is circulated through theheat exchanger. For certain therapeutic applications, the heat exchanger andassociated elements of the system have sufficient power to lower the subject'sbody temperature by at least 3 degrees C in less than 30 minutes.