An engine cooling device has a mechanical water pump, a flow rate control valve having a valve body of which a relative rotational position is changed by a motor, and a control unit that performs drive control of the motor to change the relative rotational position of the valve body to a target relative rotational position. The control unit performs protection control for setting the relative rotational position where a withstanding pressure limit rotational speed is equal to or higher than a current engine rotational speed, as a target operating position of the valve body of the flow rate control valve when the engine rotational speed rises, and performs retreat control for reducing a set range of the target relative rotational position to a prescribed retreat operation range when the supply voltage of the in-vehicle electric power supply has dropped.