NOVELTY - A polymer electrolyte membrane (PEM) fuel cell system, having a gas-cooled heat exchanger (4) for heat extraction from a reformate gas cleaning stage, is new.    USE - As a PEM fuel cell system, e.g. equipped with a methanol reformer.    ADVANTAGE - The use of a gas/gas heat exchanger employing the above specified coolants avoids the need for an additional coolant circuit with an associated liquid/air heat exchanger so that the fuel cell system has reduced size, weight and cost, avoids excessive cooling and thus termination of oxidation in the last gas cleaning stage, improves the overall efficiency of the system and avoids thermal energy losses.    DETAILED DESCRIPTION - A PEM fuel cell system has a gas generator for producing a hydrogen-rich carbon monoxide (CO) containing reformate by steam reforming and/or partial oxidation of a fuel, a gas cleaning stage for selective catalytic oxidation of the CO in the reformate and a heat exchanger for heat extraction from the gas cleaning stage. The heat exchanger is a gas-cooled heat exchanger (4) employing, as coolant, the anodic and/or cathodic off-gas from the fuel cell and/or an educt gas provided in the fuel cell system.    Preferred Features: The gas cleaning stage (2) may be a multistage operation, the gas-cooled heat exchanger (4) being associated with the last stage. A cooling medium bypass line (12) is provided parallel to the exchanger (4) and is fitted with a bypass valve (13) which is controlled by a controller (10) in accordance with preset characteristic values and/or the temperature of the coolant and/or reformate. A heat exchange surface in the gas cleaning stage is (partially) coated with catalyst for selective oxidation of CO. The reformate and the coolant pass in countercurrent in the heat exchanger (4). A dewatering unit (11), for separation of condensed water, is located downstream of the gas cleaning stage (2).    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a fuel cell system according to the invention.    Gas generator (1)    Gas cleaning stage (2)    Fuel cell (3)    Gas/gas heat exchanger (4)    Anode space (5)    Cathode space (6)    Membrane (7)    Controller (10)    Dewatering unit (11)    Bypass line (12)    Bypass valve (13)