A high-temperature operating fuel cell system comprising: a fuel cell stack that includes a cathode and an anode and generates electric power through an electrochemical reaction of an oxidant gas supplied to the cathode and a reformed gas supplied to the anode; a combustor that combusts a cathode off-gas discharged from the cathode of the fuel cell stack and an anode off-gas discharged from the anode; a heat insulator that surrounds at least part of an outer surface of the fuel cell stack and at least part of the combustor; a first preheater that covers at least part of an outer surface of the heat insulator and preheats the oxidant gas to be supplied to the fuel cell stack using heat transferred through the heat insulator; an oxidant gas feeder that supplies the oxidant gas to the first preheater; a vacuum heat insulator that covers at least part of an outer surface of the first preheater; a casing that contains the fuel cell stack and the combustor, wherein the heat insulator is located on an inner or outer surface of the casing and surrounds at least part of the outer surface of the fuel cell stack and at least part of the combustor; a sensor that detects information indicating stopping of a power generation operation of the fuel cell stack; and a controller, wherein, when the controller determines, based on a detection result from the sensor, that the power generation operation of the fuel cell stack has stopped, the controller controls the oxidant gas feeder to supply the oxidant gas to the first preheater so that the temperature of the vacuum heat insulator is equal to or lower than a prescribed temperature. a fuel cell stack that includes a cathode and an anode and generates electric power through an electrochemical reaction of an oxidant gas supplied to the cathode and a reformed gas supplied to the anode; a combustor that combusts a cathode off-gas discharged from the cathode of the fuel cell stack and an anode off-gas discharged from the anode; a heat insulator that surrounds at least part of an outer surface of the fuel cell stack and at least part of the combustor; a first preheater that covers at least part of an outer surface of the heat insulator and preheats the oxidant gas to be supplied to the fuel cell stack using heat transferred through the heat insulator; an oxidant gas feeder that supplies the oxidant gas to the first preheater; a vacuum heat insulator that covers at least part of an outer surface of the first preheater; a casing that contains the fuel cell stack and the combustor, wherein the heat insulator is located on an inner or outer surface of the casing and surrounds at least part of the outer surface of the fuel cell stack and at least part of the combustor; a sensor that detects information indicating stopping of a power generation operation of the fuel cell stack; and a controller, wherein, when the controller determines, based on a detection result from the sensor, that the power generation operation of the fuel cell stack has stopped, the controller controls the oxidant gas feeder to supply the oxidant gas to the first preheater so that the temperature of the vacuum heat insulator is equal to or lower than a prescribed temperature.