To stably perform temperature control in which temperature of a posterior combustion furnace is maintained at target temperature maintaining temperature of a furnace body at target fixed temperature.

In a control device 100, model preestimate operation is performed making the furnace body, each temperature of the posterior combustion furnace, and component amount of exhaust gas as different target values respectively, under restricted conditions in which air volume of flowage air supplied to the lower part of the furnace body 10 and air volume supplied to an center part or the lower part and the upper part or the center part of the posterior combustion furnace 30 are made control input; flow rate of fuel, air volume of flowage air, and air volume of supplied air are made control output, at least one out of flow rate of fuel, air volume of flowage air, and air volume of supplied air is kept within the prescribed range.