Abstract: By using a small heat accumulator installed in a cooling water system, malfunction of exhaust emission during warming up is prevented. Such a cooling system includes a cooling water passage for returning cooling water flowing from a cooling water outlet of an automotive engine to a cooling water inlet through a radiator, a first bypass passage for returning the cooling water just after flowing from the cooling water outlet to the cooling water inlet through the radiator, a second bypass passage for returning the cooling water just after flowing out from the cooling water outlet of the engine to the cooling water inlet through the radiator by supplying the cooling water near a heat-sensing portion of a thermostat, a flowing amount adjusting valve for enlarging a cooling water flowing ratio to the first bypass passage with respect to the second bypass passage corresponding to a reduction of a load of the engine and the heat accumulator installed through the first bypass passage.