A technique for determining whether a cooling fluid pump used for pumping a cooling fluid through a fuel cell stack has failed. The technique includes measuring the temperature of the cooling fluid at the output from the stack and/or measuring the cathode exhaust gas temperature as close as possible to the cathode outlet of the stack. The measured temperature is compared to a temperature that would be expected under the current operating conditions of the fuel cell system in a controller. If the difference between the measuring temperature and the expected temperature is large enough, then the controller provides a warning signal of pump failure, and also possibly reduces the stack outlet power.