A solid oxide fuel cell system for producing variable generated power in accordance with power demand, comprising: a fuel cell module that generates power using supplied fuel; a fuel supply device that supplies fuel to the fuel cell module; an oxidant gas supply device that supplies oxidant gas for electrical generation to the fuel cell module; a combustion portion for heating the fuel cell module by combusting residual fuel, which is remaining fuel supplied by the fuel supply device and not used for power generation; a heat storage material that is placed within the fuel cell module and stores heat produced within the fuel cell module; a demand power detection device that detects power demand; and a controller programmed to control the fuel supply device based on the demand power detected by the demand power detection device wherein a minimum value for the fuel utilization rate is high when generated power is large and is low when generated power is small, wherein the fuel utilization rate is the fraction of the fuel supply amount used to generate electricity and residual fuel not used in the electrical generation is combusted within the fuel cell module, characterized in that the controller is programmed to change the electrical power actually output from the fuel cell module with a delay after changing the fuel supply amount based on changes in demand power; wherein the controller comprises a stored heat estimating circuit that estimates the amount of surplus heat resulting from said delay between change of the fuel supply amount and change of the output of electrical power, wherein when the stored heat estimating circuit estimates that a utilizable amount of heat has accumulated in the heat storage material, the controller reduces the fuel supply amount so that the fuel utilization rate for the same generated power is increased relative to the case when a utilizable amount of heat has not accumulated wherein the controller raises the fuel utilization rate higher as the stored heat amount estimated by the stored heat estimating circuit becomes larger, and wherein the stored heat estimating circuit estimates a stored heat amount by summing addition and subtraction values reflecting the surplus heat amount resulting from said delay between change of the fuel supply amount and change of the output of electrical power.. a fuel cell module that generates power using supplied fuel; a fuel supply device that supplies fuel to the fuel cell module; an oxidant gas supply device that supplies oxidant gas for electrical generation to the fuel cell module; a combustion portion for heating the fuel cell module by combusting residual fuel, which is remaining fuel supplied by the fuel supply device and not used for power generation; a heat storage material that is placed within the fuel cell module and stores heat produced within the fuel cell module; a demand power detection device that detects power demand; and a controller programmed to control the fuel supply device based on the demand power detected by the demand power detection device wherein a minimum value for the fuel utilization rate is high when generated power is large and is low when generated power is small, wherein the fuel utilization rate is the fraction of the fuel supply amount used to generate electricity and residual fuel not used in the electrical generation is combusted within the fuel cell module, characterized in that the controller is programmed to change the electrical power actually output from the fuel cell module with a delay after changing the fuel supply amount based on changes in demand power; wherein the controller comprises a stored heat estimating circuit that estimates the amount of surplus heat resulting from said delay between change of the fuel supply amount and change of the output of electrical power, wherein when the stored heat estimating circuit estimates that a utilizable amount of heat has accumulated in the heat storage material, the controller reduces the fuel supply amount so that the fuel utilization rate for the same generated power is increased relative to the case when a utilizable amount of heat has not accumulated wherein the controller raises the fuel utilization rate higher as the stored heat amount estimated by the stored heat estimating circuit becomes larger, and wherein the stored heat estimating circuit estimates a stored heat amount by summing addition and subtraction values reflecting the surplus heat amount resulting from said delay between change of the fuel supply amount and change of the output of electrical power..