PURPOSE: To prevent any overheat which takes place after stop of circulation of cooling water in a water jacket on the block side.

CONSTITUTION: A water jacket 15 on the head side and a water jacket 14 on the block side are mutually formed independently, and an opening/closing valve 4 for leading cooling water discharged from a water pump 16 is provided on the water jacket 14 on the block side, and the cooling device is provided with a means 1 for judging an operational range where the opening/closing valve is opened/closed by the operational condition of an engine, a means 2 for storing the operational condition of the engine in a valve opening range, and a delay means 3 for delaying a valve closing operation of the opening/closing valve in response to the operation condition of the engine in the valve opening range.