Abstract: In a device for controlling the flow rate of a hydraulic operating fluid from a pump to a hydraulic motor for driving an engine cooling fan in a vehicle by modifying either the cross sectional opening area of a variable flow constriction means in the fluid conducting passage while maintaining a constant pressure difference across the flow constriction means by a pressure control valve responsive to the pressure difference across the flow constriction means or the pressure difference by selectively partly leaking the pressure transmitted from the downstream side of the flow constriction means to a rear side of the pressure control valve, a cold state relief means is provided to temporarily relieve the rear side of the pressure control valve at cold start of the engine to avoid abnormally high fluid pressure being supplied to the motor due to delayed response of the pressure control valve under high viscosity of the operating fluid at low temperature.