A pump unit comprises a primary piston pump, a secondary piston pump, and a flow path adapted for fluidically connecting in series the primary piston pump and the secondary piston pump. The pump unit's duty cycle comprises a delivery-and-fill phase, in which the primary piston pump supplies a flow of liquid to the secondary piston pump, and during the delivery-and-fill phase, the flow of liquid supplied by the primary piston pump is partly used for filling up the secondary piston pump and partly used for maintaining another flow of liquid dispensed across the secondary piston pump. The flow path comprises a heat exchanger, wherein liquid supplied by the primary piston pump passes through the heat exchanger before being supplied to the secondary piston pump. The heat exchanger is adapted for reducing a temperature difference between a temperature of liquid supplied to heat exchanger and a temperature of the secondary piston pump, in that the heat exchanger is kept at a temperature of the secondary piston pump, so that after having passed the heat exchanger, liquid supplied to the secondary piston pump has substantially the same temperature as the secondary piston pump itself.