A fuel cell system (1) includes a reformer (2), for generating a reformate gas, a fuel cell (3) for generating electric current from cathode air and reformate gas, an air supply (4), which draws in ambient air and splits this at least into reformer air and cathode air, sends the reformer air via a reformer air line (15) in the direction of the reformer and sends the cathode air via a cathode air line (16) in the direction of a cathode side (11). A recirculating line (20) connects an anode side (10) to the reformer (2). A hot gas delivery (24), which contains a hot gas path (26), is arranged in the recirculating line for driving the anode waste. A cooling air path (27), which is integrated into the cathode air line, through which the reformer air or cathode air flows, reduces thermal load of the hot gas delivery.