A thermostat is diagnosed as open failure when a specified time variation in radiator inflow water temperature from a temperature sensor mounted in a first flow path running through a radiator at a time of starting an electric water pump at a cold start of an engine is equal to or greater than a predetermined variation. In the case of open failure of the thermostat, starting the electric water pump causes cooling water from a cooling water flow path of the engine to be flowed to the first flow path, as well as to a second flow path. The radiator inflow water temperature detected by the temperature sensor mounted in the first flow path is raised by the cooling water from the cooling water flow path of the warmed engine.