Abstract: In a fuel cell stack, fuel, such as often hydrogen, electrochemically reacts with an oxidant, such as ambient air, and electric energy is generated from chemical energy. During the reaction, a proton exchange membrane (PEM) separates the fuel from the oxidant during the electrochemical process. A supply system for the fuel cell stack comprises an adjustable humidifying device for humidifying a supply gas which is supplied to the fuel cell stack, as a function of a control signal; and a dehumidifying device, which is configured to dehumidify an exhaust gas that is formed from the supply gas conducted through the fuel cell stack, and to discharge the same as a dehumidified exhaust gas. A controller, which generates the control signal, is configured from a programming and/or switching point of view to generate the control signal based on the gas temperature of the dehumidified exhaust gas.