Abstract: A cooling system for an internal combustion engine has a water jacket connected to a radiator with upper and lower radiator passages for cooling coolant leaving the engine and a water pump in the lower radiator passage for circulating coolant through the water jacket. A bypass passage connects the upper radiator passage to the lower radiator passage for the circulation of coolant through the water jacket bypassing the radiator. A first thermostat valve in the upper radiator passage closes the upper radiator passage and opens the bypass passage when the coolant is lower than a predetermined low temperature and the engine is operated in a low engine load range so as to permit the circulation of coolant through the bypass passage bypassing the bypass passage.