A system for storing and cooling milk includes a cooling tank to store milk, a first sensor monitoring the filling level of milk in the cooling tank, and a cooling system cooling the milk in the cooling tank including a cooling device, a second sensor, and a control device. The cooling device includes an evaporator, a varying-capacity modulated scroll compressor connected with its suction side to the evaporator, a condenser connected to the high pressure side of the compressor, and an expansion valve interconnected between the condenser and the evaporator. The second sensor monitors a parameter indicative of the pressure at the suction side of the compressor. The control device is operatively connected to the first sensor to receive the monitored filling level, the second sensor to receive the monitored parameter, and the compressor to control the capacity thereof in response to the monitored filling level and the monitored parameter.