A solid oxide fuel cell for producing variable power in response to power demand, comprising: a fuel cell module configured to generate electricity using supplied fuel; a fuel supply device configured to supply fuel to the fuel cell module; an oxidant gas supply device configured to supply oxidant gas for electrical generation to the fuel cell module; a combustion section configured to burn remaining residual fuel supplied by the fuel supply device and not utilized for electrical generation, and heating the interior of the fuel cell module; a heat storing material placed within the fuel cell module and configured to accumulate heat generated within the fuel cell module; a power demand detection device configured to detect power demand; a temperature detection device configured to detect the temperature of the fuel cell module; and a control device programmed to control the fuel cell, based on the power demand detected by the power demand detection device, such that the fuel utilization rate, which is the fraction of the fuel actually used to generate electricity relative to the fuel supply rate, is high when generated power is larger, and the fuel utilization rate is low when generated power is smaller, characterised in that the control device is also programmed to increases the power actually output from the fuel cell module at a predetermined delay after increasing the fuel supply rate in response to an increment in power demand; wherein the control device includes a stored heat estimating circuit configured to estimate the amount of stored heat accumulated in the heat storing material based on the detected temperature detected by the temperature detection device, and the control device reduces the fuel supply rate so that the fuel utilization rate increases relative to the same generated power when it is estimated that a usable amount of heat has accumulated in this heat storing material, in comparison with cases in which it is estimated that a usable amount of heat has not accumulated and wherein the stored heat estimating circuit estimates the amount of stored heat stored in the heat storing material based on detected temperature history. a fuel cell module configured to generate electricity using supplied fuel; a fuel supply device configured to supply fuel to the fuel cell module; an oxidant gas supply device configured to supply oxidant gas for electrical generation to the fuel cell module; a combustion section configured to burn remaining residual fuel supplied by the fuel supply device and not utilized for electrical generation, and heating the interior of the fuel cell module; a heat storing material placed within the fuel cell module and configured to accumulate heat generated within the fuel cell module; a power demand detection device configured to detect power demand; a temperature detection device configured to detect the temperature of the fuel cell module; and a control device programmed to control the fuel cell, based on the power demand detected by the power demand detection device, such that the fuel utilization rate, which is the fraction of the fuel actually used to generate electricity relative to the fuel supply rate, is high when generated power is larger, and the fuel utilization rate is low when generated power is smaller,