An exhaust air guide of a fuel cell stack is provided, in particular in a motor vehicle, with a cooling device which belongs to the functional environment of the fuel cell stack and is in the form of a cooler structure through which ambient air flows. At least some of the exhaust air of the fuel cell stack is guided into the cooler structure or behind the cooler structure, as viewed in the direction of flow of the ambient air through the cooler structure, to such an extent that, at the cooler structure, the exhaust air flow brings about an increase in the mass flow of the ambient air through the cooler structure in accordance with the jet pump principle or, at the cooler structure, the exhaust air flow, in accordance with the jet pump principle, brings about a pressure difference conveying at least a portion of the ambient air through the cooler structure.