An extracorporeal blood treatment system comprising - a stationary system area including among other components: a water treatment unit, preferably of the reverse osmosis type, whose outlet has connected thereto at least one water supply line that opens into at least one line section provided with a number of branch connections and at least one drain line through which exhausted blood treatment/dialysis fluid can be discharged, and further comprising - a non-stationary system area including: a number of blood treatment machines fluidly coupled to the branch connections and the at least one drain line in a selective manner, wherein - a stationary heating unit disposed externally to the blood treatment machine and comprising a first heat exchanger having one side (WT1/1) thereof connected to the at least one water supply line between the water treatment unit and the line section including the branch connections, and having the other side (WT1/2) thereof connected to the at least one drain line, and - a central electronic control unit which is electrically connected to the blood treatment machines fluidly coupled at the time in question so as to obtain information on at least the prevailing operating phases of these machines and configured to, in accordance with this information, control the stationary heating unit such that a target temperature is adjusted in the at least one water supply line, and - the central electronic control unit has connected thereto at least one temperature sensor (T1-T4), which measures the actual temperature in the water supply line at least between the first heat exchanger and the line section including the branch connections and which controls in accordance therewith the stationary heating unit so as to accomplish the target temperature, characterized in that the electronic control unit intervenes in the operating sequence of the blood treatment machines fluidly coupled at the time in question, so as to coordinate their prevailing operating phases such that operating phases with high electric power consumption are performed with a time shift such that they temporally overlap one another as little as possible. - a stationary system area including among other components: a water treatment unit, preferably of the reverse osmosis type, whose outlet has connected thereto at least one water supply line that opens into at least one line section provided with a number of branch connections and at least one drain line through which exhausted blood treatment/dialysis fluid can be discharged, and further comprising a water treatment unit, preferably of the reverse osmosis type, whose outlet has connected thereto at least one water supply line that opens into at least one line section provided with a number of branch connections and at least one drain line through which exhausted blood treatment/dialysis fluid can be discharged, and further comprising - a non-stationary system area including: a number of blood treatment machines fluidly coupled to the branch connections and the at least one drain line in a selective manner, wherein a number of blood treatment machines fluidly coupled to the branch connections and the at least one drain line in a selective manner, wherein - a stationary heating unit disposed externally to the blood treatment machine and comprising a first heat exchanger having one side (WT1/1) thereof connected to the at least one water supply line between the water treatment unit and the line section including the branch connections, and having the other side (WT1/2) thereof connected to the at least one drain line, and - a central electronic control unit which is electrically connected to the blood treatment machines fluidly coupled at the time in question so as to obtain information on at least the prevailing operating phases of these machines and configured to, in accordance with this information, control the stationary heating unit such that a target temperature is adjusted in the at least one water supply line, and - the central electronic control unit has connected thereto at least one temperature sensor (T1-T4), which measures the actual temperature in the water supply line at least between the first heat exchanger and the line section including the branch connections and which controls in accordance therewith the stationary heating unit so as to accomplish the target temperature,