A milking system comprises a milking device for milking a milking from a dairy animal during a milking session, and is provided with a control unit for the milking system, milking cups, a first milk jar for receiving the milking, a first pumping device for pumping the milking from the first milk jar to a first milk pipe, a second milk jar in flow communication with the first milk pipe for receiving the milking from the first milk jar therefrom, and a second pumping device for pumping the milking from the second milk jar into a second milk pipe. The first pumping device is configured to pump the milking at a first flow rate and the second pumping device is configured to pump the milking at a second flow rate, which is lower than the first flow rate. The milking system furthermore comprises a heat- exchanging system in flow communication with the second milk pipe for receiving the milking pumped in the second milk pipe and for bringing the received milking to a desired temperature. The capacity of the milking system is maintained by pumping the milking directly after a milking, but by collecting this milking in the second milk jar and pumping it relatively slowly and steadily, the milk quality is maintained more reliably. In addition, a downstream heat exchanger can then be made smaller. Also, it is then easier to change the desired temperature.La présente invention concerne un système de traite qui comprend un dispositif de traite pour traire le lait d'un animal laitier pendant une session de traite, et est pourvu d'une unité de commande pour le système de traite, de manchons trayeurs, d'un premier pot de lait pour recevoir la traite, d'un premier dispositif de pompage pour pomper la traite du premier pot de lait vers un premier tuyau de lait, d'un deuxième pot de lait en communication fluidique avec le premier tuyau de lait pour recevoir la traite du premier pot de lait depuis celui-ci, et d'un deuxième dispositif de pompage pour pomper la traite du deuxième pot de
