The invention provides an improved fuel cell system and a method of operating a fuel cell, which ensure that the fuel cell can be operated at high efficiency without irreversible damage. The fuel cell system according to the invention has at least one fuel cell with a fuel cell stack and with separator plates, which are equipped with inlets and outlets for a heat transfer medium, a thermostat, a heat transfer medium circuit, which has a transport device for the heat transfer medium and includes at least the fuel cell and the thermostat, at least one temperature sensor for the fuel cell and a monitoring and control unit for the temperature of the fuel cell. With the invention it is possible to operate the fuel cell in a range close to the preset optimum operating temperature.