A flow control valve is located in a coolant circuit that extends through an engine. The flow control valve is operated in accordance with a control mode selected from a full closing control mode, a full opening control mode, and a feedback control mode. When switching from one control mode to another, the flow control valve is controlled in accordance with a transitional control procedure selected from different types of transitional control procedures. The transitional control procedure to be performed is selected depending on which control modes are performed before and after the control mode switching and/or the current condition of the engine. Transitional controlling of the flow control valve is thus appropriately conducted.