To more correctly estimate the temperature of the exhaust gas of an internal combustion engine of an automobile.

A regular exhaust temperature Ti* that is an exhaust temperature estimated at the regular operation of the engine in current operation conditions is set (S100). An anneal constant n is set so as to tend to be smaller as the amount Qa of intake air is larger and to be larger in deceleration as compared to not in deceleration (S120 to S140). An estimated exhaust temperature Tiest is calculated by providing the regular exhaust temperature Ti* with anneal treatment in which the larger anneal constant n set tends to cause the estimated exhaust temperature Tiest to be more moderately changed (S150).