A control device for a fuel cell system has a fuel cell body, a fuel gas supply system supplying fuel gas to the fuel cell body in dependence on a demanded power output of the fuel cell body; an air supply system supplying air to the fuel cell body in dependence on the demanded power output, a combustor combusting exhaust gases exhausted from the fuel cell body, a temperature sensor sensing a temperature of the combustor, a discriminator section discriminating whether an increase in the temperature as sensed is equal to or above a predetermined threshold value when the demanded power output increases, and a permitting section permitting the power output available from the fuel cell body to be increased when the discriminator section discriminates that the increase in the temperature as sensed is equal to or above the predetermined threshold value.