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