When the passing of coolant in an internal combustion engine (1) is restricted to accelerate the warm-up of the internal combustion engine (1) and the coolant in this engine (1) is undergoing nucleate boiling, the restriction of the passing of the coolant in the internal engine (1) is maintained. Specifically, the restriction of the passing of the coolant in the internal combustion engine (1) is maintained during nucleate boiling from the beginning of nucleate boiling of the coolant in the internal combustion engine (1) until the maintenance period has elapsed. Thus, the warm-up of the internal combustion engine (1) is effectively accelerated by restricting the passing of the coolant in the engine (1). Furthermore, the restriction of the passing of the coolant in the internal combustion engine (1) is canceled when the maintenance period has elapsed. Thus, low-temperature coolant flows in the internal combustion engine (1) and the internal combustion engine (1) is cooled by this coolant, so nucleate boiling of the coolant in the engine (1) is suppressed.