A control system for a hydraulic tandem pump assembly including a primary pump for supplying fluid under pressure to a power-assisted steering device and a secondary pump for supplying fluid under pressure to a hydraulic motor of an engine cooling fan, which pumps are mounted on a common drive shaft for rotation therewith. The control system includes an electrically operated flow quantity control valve disposed within a communication passage between the secondary pump and the hydraulic motor to bypass fluid under pressure discharged from the secondary pump into an inlet passage connecting a fluid reservoir to the secondary pump, a temperature sensor arranged to detect an ambient temperature of a prime engine of the vehicle for producing therefrom an output signal indicative of the ambient temperature, and an electric control apparatus connected to the sensor to control an electric current applied to the control valve in response to the output signal from the sensor in such a manner that the control valve is conditioned to bypass a large part or the entirety of fluid under pressure discharged from the secondary pump into the inlet passage when the ambient temperature of the engine is below a predetermined value.