Apparatus for cooling a fuel cell stack. The cooling system uses vaporization cooling of the fuel stack and supersonic vapor compression of the vaporized coolant to significantly increase the temperature and pressure of the liquid coolant flowing through a heat exchanger. By increasing the heat rejection temperature of the coolant delivered to the heat exchanger, the heat transfer area of the heat exchanger can be reduced and the mass flow rate of coolant can also be reduced. The increased fluid pressure is used to circulate the coolant through the cooling system, thereby eliminating the circulation pump associated with conventional systems.