The system comprises a central microcomputer (1), a power source (14) equipped with means of back-up in the event of failure of the network; it further comprises terminals (50-53) each allocated to one real estate dwelling. These terminals include inputs (50a) for temperature sensors, outputs (50b) for electrovalves in the heating fluid circuits, a display (50c) and a keyboard (50d) for entering setpoints. The microcomputer (1) is made to communicate sequentially with each of the terminals, in order to determine the electrovalve controls as a function of the requirements detected by the sensors, as a function of entered setpoints. The sequential communication is effected via a thirty-two channel main concentrator (2) and satellite concentrators (3, 4). The concentrators (2, 3, 4) supply the terminals (50-53) with the energy required for their operation, from their own sources (14, 32, 42). The use of satellite concentrators (3, 4) endows the system with a very flexible configuration allowing a reduction in the length of the lines and in the size of the bundles. The system allows accessory management of services and alarms.