In a cooling system of an internal combustion engine, coolant flowing through a radiator and bypassing the radiator are mixed in a flow control valve controlled by ECU on the basis of signals provided by sensors such as a coolant temperature sensor, so that the coolant is circulated by an electric pump to control the coolant temperature for the internal combustion engine. A desired coolant temperature is changed according to the operating condition of the internal combustion engine, the traveling condition of a vehicle and the ambient condition. A fluid control valve controls the flow rate of cooling water through the bypass passage. The flow control valve is diagnosed for abnormalities. If it is determined that the flow control valve is in an abnormal condition, a heat generation rate reducing control operation is executed to reduce the heat generation rate of the internal combustion engine.