Cooling system and method of internal combustion engine

A cooling system and method of an internal combustion engine includes a heat accumulating container, wherein a flow path is switched by a three-way switching valve 25 so that the cooling water flows to a heat accumulating container 29 from a combustion heater 21 before cranking at a start of an engine 1, and a discharge quantity of a second water pump 19 is increased by rotating a drive motor for a second water pump 19 at a high speed, thereby enabling the engine 1 to be quickly warmed up at the start of the engine 1. With this contrivance, the high-temperature cooling waterreserved in the heat accumulating container 29 flows at a high speed through a cooling water passageway 3 of the engine 1, and a heat transfer coefficient between the cooling water and a wall surface of the engine 1 increases, thus quickly heating the engine 1.