Blood treatment/dialysis systems are disclosed. The systems include a water treatment unit, preferably of the reverse osmosis type, whose outlet has connected thereto a water supply line provided with a number of branch connections having fluidly coupled thereto blood treatment/dialysis machines in a selective manner, and a drain line through which exhausted blood treatment fluid can be discharged from fluidly coupled blood treatment/dialysis machines. Also disclosed is a machine-external heat exchanger, which is connected to the water supply line upstream of the branch connections on one side and to the drain line on the other side.