A fuel cell system (10) comprises a fuel cell (14) and an evaporative cooling system (16), which is in thermal contact with the fuel cell (14), in order that heat generated by the fuel cell (14) during operation of the fuel cell (14) is absorbed through evaporation of a cooling medium and is removed from the fuel cell (14). The fuel cell system (10) further comprises a device (22) for sensing the pressure in the evaporative cooling system (16). A control unit (24) is adapted to control the operating temperature of the fuel cell (14) in dependence on signals that are supplied to the control unit (24) from the device (22) for sensing the pressure in the evaporative cooling system (16), in such a way that the cooling medium of the evaporative cooling system (16) is transferred from the liquid to the gaseous state of matter by the heat generated by the fuel cell (14) during operation of the fuel cell (14).