NOVELTY - A fuel cell system (10) comprises a fuel cell stack (34) formed by stacking solid oxide fuel cells (32) comprising stacked electrolyte electrode assembly (30) and a separator, a first heat exchanger (36), a reformer (40), a first heating mechanism (92), a second heating mechanism (94), a second heat exchanger (25), a flow rate regulator valve (74), and a control mechanism (24). The electrolyte electrode assembly includes an anode (28a), a cathode (28b), and an electrolyte (26) in between.    USE - A fuel cell system used in a vehicle.    ADVANTAGE - The fuel cell system reliably carries out the thermally self-sustained operation even in a partial load operation, and improves the heat efficiency.    DETAILED DESCRIPTION - A fuel cell system comprises a fuel cell stack formed by stacking solid oxide fuel cells comprising stacked electrolyte electrode assembly and a separator; a first heat exchanger for heating an oxygen-containing gas; a reformer for a mixed fuel of raw fuel containing hydrocarbon and water vapor to produce a fuel gas; a first heating mechanism for supplying part of an exhaust gas discharged from the fuel cell stack after consumption in power generation reaction, to the reformer; a second heating mechanism for supplying the remaining exhaust gas, to the first heat exchanger, as a heat medium for heating the oxygen-containing gas, and supplying heat generated in the first heat exchanger to the reformer; a second heat exchanger; a flow rate regulator valve; and a control mechanism for controlling the flow rate regulator valve. The electrolyte electrode assembly includes an anode, a cathode, and an electrolyte in between. An INDEPENDENT CLAIM is included for a method of operating a fuel cell system.    DESCRIPTION OF DRAWING(S) - The drawing is a diagrammatic view of a gas extraction circuit of the fuel cell system.    Fuel cell system (10)    Control mechanism (24)    Second heat exchanger (25)    Electrolyte (26)    Anode (28a)    Cathode (28b)    Electrolyte electrode assembly (30)    Solid oxide fuel cells (32)    Fuel cell stack (34)    First heat exchanger (36)    Reformer (40)    Flow rate regulator valve (74)    First heating mechanism (92)    Second heating mechanism (94)