Abstract: A pumping system (100*) having a pump (10*), such as a variable-displacement vane pump (10*) or a gear pump. The pump (10*) in turn has hydraulic pressure-control dissipating devices (29, 30) for imparting to the oil in a first control chamber (22) a pressure (p2) lower than the pressure of a second chamber (20). The system (100*) is characterized in that the first control chamber (22) of the pump (10*) has a channel (40) connecting the first control chamber to an oil inlet (23). And the channel (40) has an opening/closing device (41) controlled selectively by an engine operating parameter, such as oil temperature.