A control apparatus which is configured to control a fuel cell unit provided with a power generation unit which is configured to generate power upon chemical reaction and auxiliaries which are configured to assist an operation of the power generation unit, and a storage battery unit which has a storage battery charged by power supplied from a grid or the power generation unit, comprising: a control unit which is configured to instruct an operation mode of the fuel cell unit to the fuel cell unit, wherein the operation mode of the fuel cell unit includes: a power generation mode for aggressively performing the power generation by the power generation unit, wherein the power generation mode includes a load following mode and a rated power generation mode in which the power consumption of the auxiliaries and the power consumption of the load are covered by the power output from the power generation unit and in which in the rated power generation mode surplus power is supplied to the storage battery; and a constant temperature mode for performing a control to cover a power consumption of the auxiliaries by power supplied from outside and a control to keep a temperature of the power generation unit within a predetermined temperature range, where the power output from the power generation unit is smaller than the power consumption of the auxiliaries, and the control unit is configured to instruct to change the operation mode of the fuel cell unit to the constant temperature mode so that the storage battery is charged by the power supplied from the grid, when the storage battery is charged and when a power buying unit price from the grid falls below a predetermined value, wherein the amount of fuel to be supplied to the power generation unit in the constant temperature mode is smaller than the amount of fuel to be supplied to the power generation unit in the power generation mode, characterized in that the predetermined value is a power generation unit price of the power generation unit in the rated power generation mode for controlling power output from the power generation unit, wherein the predetermined temperature range in the constant temperature mode is 450 °C to 600 °C, wherein the operation mode of the fuel cell unit further includes an idling mode in which the power output from the power generation unit is not supplied to a load and the temperature of the power generation unit is kept at a power generation temperature, wherein in the idling mode the power consumption of the auxiliaries is covered by the power output from the power generation unit and the output power of the fuel cell unit is controlled to be zero, wherein the predetermined temperature range in the constant temperature mode is lower than the power generation temperature in the power generation mode and the idling mode. a control unit which is configured to instruct an operation mode of the fuel cell unit to the fuel cell unit, wherein the operation mode of the fuel cell unit includes: a power generation mode for aggressively performing the power generation by the power generation unit, wherein the power generation mode includes a load following mode and a rated power generation mode in which the power consumption of the auxiliaries and the power consumption of the load are covered by the power output from the power generation unit and in which in the rated power generation mode surplus power is supplied to the storage battery; and a constant temperature mode for performing a control to cover a power consumption of the auxiliaries by power supplied from outside and a control to keep a temperature of the power generation unit within a predetermined temperature range, where the power output from the power generation unit is smaller than the power consumption of the auxiliaries, and the control unit is configured to instruct to change the operation mode of the fuel cell unit to the constant temperature mode so that the storage battery is charged by the power supplied from the grid, when the storage battery is charged and when a power buying unit price from the grid falls below a predetermined value, wherein the amount of fuel to be supplied to the power generation unit in the constant temperature mode is smaller than the amount of fuel to be supplied to the power generation unit in the power generation mode, characterized in that the predetermined value is a power generation unit price of the power generation unit in the rated power generation mode for controlling power output from the power generation unit, wherein the predetermined temperature range in the constant temperature mode is 450 °C to 600 °C, wherein the operation mode of the fuel cell unit further includes an idling mode in which the power output from the power generation unit is not supplied to a load and the temperature of the power generation unit is kept at a power generation temperature, wherein in the idling mode the power consumption of the auxiliaries is covered by the power output from the power generation unit and the output power of the fuel cell unit is controlled to be zero, wherein the predetermined temperature range in the constant temperature mode is lower than the power generation temperature in the power generation mode and the idling mode.