Abstract: Air-conditioning installation for room spaces (1), comprising a heat transfer device (4) for preheating supply air (A) by transferring heat from exhaust air (B) into the supply air; heating means including a heating source (11) for further heating the supply air; cooling means including a cooling source (14) for cooling the supply air; and adjusting means (16, 17, 18, 21, 32, 33, 34) for sensing the temperature of the supply air and for controlling the heat transfer device and the heating and cooling means on the basis of the sensed temperature. To simplify the structure of the installation, the heating and cooling sources (11, 14) are connected to the heat transfer device (4) so that the preheating, further heating and cooling of the supply air take place through the common heat transfer device.