A catheter has an inner sleeve through which refrigerant circulates to and from a source of refrigerant. The catheter also has an outer sleeve surrounding the inner sleeve, including a distal end thereof. The outer sleeve is filled with a frozen biocompatible substance. The refrigerant is separated from the biocompatible substance by one or more walls of the inner sleeve such that the refrigerant is isolated from a patient in whom the catheter is positioned by both the inner sleeve and the frozen biocompatible substance. The refrigerant circulates through the catheter when the catheter is positioned in the patient to maintain the biocompatible substance frozen as heat is transferred from the patient to the biocompatible substance.