A system is used for cooling a fuel cell arrangement, particularly a fuel cell arrangement with a gas generating system in a motor vehicle. A coolant circuit for the system is connected to a cooler, a coolant delivery device, a fuel cell and at least another component to be cooled. The coolant circuit has at least two valve devices which are each assigned to the fuel cell and the at least another component to be cooled. By means of the valve devices, a flow rate of the coolant through the fuel cell or the another component to be cooled can be influenced as a function of the temperature in the region associated with the fuel cell or the another component.