the present invention relates to a milking system that comprises a milking device for milking a dairy animal during a milking session, and is equipped with a milking system control unit, milking cups, a first milk jar to receive milking, a first pumping device to pump milking from the first milk jar to a first milk tube, a second milk jar in flow communication with the first milk tube to receive milking from the first jar of milk, and a second pumping device to pump the milk from the second milk jar into a second milk tube. the first pumping device is configured to pump milking at a first flow rate and the second pumping device is configured to pump milking at a second flow rate, which is less than the first flow rate. in addition, the milking system comprises a heat exchange system in flow communication with the second milk tube to receive the milked pumped into the second milk tube and to drive the received milking to a desired temperature. the capacity of the milking system is maintained by pumping the milking directly after milking, however, collecting this milking in the second milk jar and pumping it relatively slowly and steadily, the quality of the milk is maintained more reliably. in addition, a downstream heat exchanger can then be reduced. also, it is easier to change the desired temperature.a presente invenção refere-se a um sistema de ordenha que compreende um dispositivo de ordenha para ordenhar um animal leiteiro durante uma sessão de ordenha, e é dotado de uma unidade de controle do sistema de ordenha, copos de ordenha, uma primeira jarra de leite para receber a ordenha, um primeiro dispositivo de bombeamento para bombear a ordenha a partir da primeira jarra de leite para um primeiro tubo de leite, uma segunda jarra de leite em comunicação de fluxo com o primeiro tubo de leite para receber a ordenha da primeira jarra de leite, e um segundo dispositivo de bombeamento para bombear a ordenha da segunda jarra de leite em um segundo tubo de leite. o prime
