When the passing of coolant in an internal combustion engine is restricted to accelerate the warm-up of the internal combustion engine and the coolant in this engine is undergoing nucleate boiling, the restriction of the passing of the coolant in the internal engine is maintained. Specifically, the restriction of the passing of the coolant in the internal combustion engine is maintained during nucleate boiling from the beginning of nucleate boiling of the coolant in the internal combustion engine until the maintenance period has elapsed. Thus, the warm-up of the internal combustion engine is effectively accelerated by restricting the passing of the coolant in the engine. Furthermore, the restriction of the passing of the coolant in the internal combustion engine is canceled when the maintenance period has elapsed. Thus, low-temperature coolant flows in the internal combustion engine and the internal combustion engine is cooled by this coolant, so nucleate boiling of the coolant in the engine is suppressed.