The present invention relates to a fuel cell system (1a; 1b; 1c; 1d) comprising: at least one fuel cell stack (2) with an anode portion (3) and a cathode portion (4); a reformer-heat exchanger (5) with a cold side which is upstream of the anode portion (3) and forms a reformer (6) and a hot side which is downstream of the cathode portion (4) and forms a heat exchanger (7); and an afterburner (8) downstream of the heat exchanger (7) for combusting anode exhaust gas from the anode portion (3) and/or cathode exhaust gas from the cathode portion (4), the heat exchanger (7) being situated directly downstream of the cathode portion (4) and being in fluid communication with the cathode portion (4) by means of a cathode exhaust gas line (9) in order for the cathode exhaust gas to be fully conducted through the heat exchanger (7). The invention also relates to a method for controlling the temperature of a fuel cell system (1a; 1b; 1ce; 1d) according to the invention.