A method of cooling an organ. A portion of a body fluid bathing an organ is withdrawn while a cool fluid is infused. A separate portion of the body fluid can be cooled during the withdrawing. A volume of up to about 5% of the body fluid can be withdrawn. A catheter is provided with a cooling mechanism to contact and cool the body fluid. The catheter can have an inlet port to withdraw body fluid and an outlet port to allow infusion of a cool fluid. Additionally, an organ cooling pump assembly is provided including a pump and a catheter.