cooling water is circulated at small flow rate of 1 to 5 l / min between a bypass passage and an engine without circulating the cooling water in an oil cooler before the warming - up of the engine is completed . after the warming - up is completed , the cooling water is supplied to the oil cooler so that the engine cooling water temperature is maintained at 95 ° c . to 110 ° c . consequently , the no local boiling of the cooling water in the engine occurs to prevent the engine from being deformed locally due to heat . thus , the warming - up of the engine can be promoted while preventing the heat of the engine from being absorbed by the atf through the cooling water . after the warming - up is completed , the fuel consumption can be improved by reducing the friction loss of the engine oil .