A patient temperature control catheter (10) includes working fluid supply (16) and return (18) lumens through which working fluid circulates to exchange heat with a patient in whom the catheter is positioned. At least one lumen is defined by plural coils (32) axially spaced from each other. At least a first coil is a large coil that inflates with working fluid to seat against a wall of a blood vessel in which the catheter is positioned, with blood flowing through the coil so as not to block blood flow in the vessel. Alternate centering structures (116) are disclosed.