PROBLEM TO BE SOLVED: To avoid excessive regulation by guaranteeing, at costs which are reduced as further as possible, a bottom exhaust temperature Tein in an inlet to a pressure wave supercharger.SOLUTION: An exhaust system 10 between an exhaust temperature Ta provided by an engine control device and an inlet to a pressure wave supercharger 2 is represented as a heat model and stored in the engine control device. After modeling on the basis of the provided exhaust temperature Ta, the exhaust temperature Tein in the inlet to the pressure wave supercharger 2 is assumed by the heat model. The assumed exhaust temperature Tein is compared with a limit temperature Tgrenz stored in the engine control device and if the assumed exhaust temperature is lower than the limit temperature Tgrenz, the quantity of required heating output is determined. Thereafter, heating processing is executed for elevating the assumed exhaust temperature Tein till the assumed exhaust temperature Tein does not become lower than the limit temperature Tgrenz any more.