An extracardiac pumping system and method for using it supplement the circulation of blood, including the cardiac output, in a patient without any component thereof being connected to the patient's heart. A battery powered pump may be implanted subcutaneously and attached to an inflow conduit fluidly coupled to a patient's femoral artery via a subcutaneous anastomosis connection. The pump draws blood from the inflow conduit and discharges it through an outflow conduit fluidly coupled to a second peripheral artery via another subcutaneous anastomosis connection. The battery may be charged extracorporeally and the pump may be operated in either a continuous or pulsatile fashion in synchronization with the patient's heart. The conduits can be housed in a multi-lumen catheter and a reservoir may be provided which fluidly communicates with the inflow conduits. An additional feature may keep blood traveling extracorporeally within the system at or near body temperature. The system is capable of adjusting outflow from the pump to optimize the mixing of red blood cells in the aorta and thereby enhance oxygen delivery to tissues by minimizing blood cell concentration in the center of the aorta.