An engine 10 includes variable valve mechanisms 36 and 38 and a variable compression ratio mechanism 40. An ECU 60 executes temperature balance control when a fuel-cut operation is executed. In the temperature balance control, valve opening characteristics of an exhaust valve 34 are controlled based on a magnitude relation between an actual catalyst temperature Ts and a target catalyst temperature (T1 or T2) and a magnitude relation between a water temperature Thw and a required cylinder wall temperature Ty. When executing a fuel-cut operation, it is thereby possible to control both the actual catalyst temperature Ts and the water temperature Thw in a well-balanced manner so that the actual catalyst temperature Ts falls within a temperature range (T1 to T2) suitable for operation of the catalysts 24 and 26, and the water temperature Thw becomes close to the required cylinder wall temperature Ty.
