Method for heating or cooling rooms of a building with a temperature-control system, wherein the temperature-control system comprises: a) a central heat generator or cold generator with a multiple circuit circulation system having a supply pipe and a return pipe; b) a central circulation pump for the circulation of a temperature-control fluid in the multiple circuit circulation system; c) at least two heat exchanger devices, each of which thermally supplies one room of the building and each of which is connected to the supply pipe and to the return pipe of the multiple circuit circulation system; d) one valve each with actuator per heat exchanger unit; e) one room temperature sensor each per thermally supplied room; and f) a central control and regulation unit, which is connected to the actuators of the valves as well as to the room temperature sensors; wherein with the heating or cooling in the thermally supplied rooms of the building a temperature transition is carried out from an initial state to a final state different from the initial state with corresponding room temperature setpoint values, characterized in that the temperature transition is carried out according to the following algorithm with at least two preselected temperature levels lying between the initial state and the final state, wherein: i) all valves are first opened completely by the central control and regulation unit; ii) as soon as the temperature in a room reported by the corresponding room temperature sensor has reached a first temperature level, the valve concerned is closed completely; iii) as soon as this first temperature level is also reached in the next room, that valve is also closed completely; iv) the same procedure is applied to each additional room until this first temperature level is also reached in a last room; v) then all valves are fully opened again until a second temperature level is reached in one room, whereupon the respective valve is fully closed, and the procedure continues until this second temperature level is reached in a last room as well; vi) all valves are fully opened again and the algorithm continues until all thermally supplied rooms have reached their room temperature setpoint value; vii) after reaching a room temperature setpoint value, a regulation phase follows in which the temperature in the room concerned is maintained by the central control and regulation unit at an end temperature level corresponding to the room temperature setpoint value. a) a central heat generator or cold generator with a multiple circuit circulation system having a supply pipe and a return pipe; b) a central circulation pump for the circulation of a temperature-control fluid in the multiple circuit circulation system; c) at least two heat exchanger devices, each of which thermally supplies one room of the building and each of which is connected to the supply pipe and to the return pipe of the multiple circuit circulation system; d) one valve each with actuator per heat exchanger unit; e) one room temperature sensor each per thermally supplied room; and f) a central control and regulation unit, which is connected to the actuators of the valves as well as to the room temperature sensors; i) all valves are first opened completely by the central control and regulation unit; ii) as soon as the temperature in a room reported by the corresponding room temperature sensor has reached a first temperature level, the valve concerned is closed completely; iii) as soon as this first temperature level is also reached in the next room, that valve is also closed completely; iv) the same procedure is applied to each additional room until this first temperature level is also reached in a last room; v) then all valves are fully opened again until a second temperature level is reached in one room, whereupon the respective valve is fully closed, and the procedure continues until this second temperature level is reached in a last room as well; vi) all valves are fully opened again and the algorithm continues until all thermally supplied rooms have reached their room temperature setpoint value; vii) after reaching a room temperature setpoint value, a regulation phase follows in which the temperature in the room concerned is maintained by the central control and regulation unit at an end temperature level corresponding to the room temperature setpoint value.