A catheter is adapted to exchange heat with a body fluid, such as blood, flowing in a body conduit, such as a blood vessel. The catheter includes a shaft with a heat exchange region disposed at its distal end. This region may include hollow fibers which are adapted to receive a remotely cooled heat exchange fluid preferably flowing in a direction counter to that of the body fluid. The hollow fibers enhance the surface area of contact, as well as the mixing of both the heat exchange fluid and the body fluid. The catheter can be positioned to produce hypothermia in a selective area of the body or alternatively positioned to systemically cool the entire body system.