An engine cooling system has an engine water jacket, a coolant circulation passage connecting a water jacket outlet to a water jacket inlet and a radiator disposed in the coolant circulation passage. A thermostat valve selectively closes and opens the coolant circulation passage leading to the radiator. A bypass passage extends from between the water jacket outlet and the thermostat valve to an outlet side of the radiator. A bridge passage connects a portion of the bypass passage to a portion of the coolant circulation passage located downstream of the radiator and upstream of where the bypass passage merges therewith. A resistance generating section is located downstream of the bridge passage connection to the coolant circulation passage and upstream of the bypass passage connection to the coolant circulation passage. The bridge passage has an oil heat exchanger to exchange heat between the cooling medium and transmission oil passing therethrough.