An automatic milking system comprising at least one milking robot assembly with a milking robot and a milk cooling apparatus. The milk cooling apparatus comprises a first and a second heat exchanger both of which are fluidly connected to a water supply. The second heat exchanger cools the water of the water supply and feeds it to the first heat exchanger which uses the cooled water to cool milk from the milking robot. Moreover the invention relates to a milking robot and a milking robot assembly both of which is suitable for use in the automatic milking system.