Catheter devices and methods for intravascular heating and/or cooling of human or veterinary patients. The catheter devices generally comprise catheters having inflow and outflow lumens and at least one curvilinear balloon connected to the inflow and outflow lumens such that heat exchange fluid may be circulated through the balloon(s). The catheter is inserted into the vasculature and heated or cooled fluid is circulated through the balloon(s) to heat or cool blood flowing in heat-exchange proximity to the balloon(s), thereby effecting heating or cooling of all or a portion of the patient's body.