If an engine undergoes high-load operations immediately after start up from its cold state, a thermostat is closed to inhibit passage of cooling water through the inside of the engine, and the cooling water stagnant in a cylinder head receives heat from a combustion chamber. Therefore, the cooling water will possibly boil. However, the thermostat is formed in such a manner that a valve body may be opened forcedly if the discharge flow rate of a water pump is greater than the flow rate in a normal use region. Therefore, in such a situation, the discharge flow rate of the water pump is increased greater than the flow rate in the normal use region to open the valve body with good response, thereby passing water into the engine quickly. This configuration prevents the cooling water stagnant in the cylinder head from boiling before the valve body is opened completely.