An air-conditioning apparatus regulates at least the temperature of at least one room to a predetermined temperature desired value (T_{RAUM SOLL}) by ventilation with heated or cooled supply air. The air-conditioning apparatus has a supply air motor (15) which feeds the supply air through a supply air channel (10) to the room (1) to be air-conditioned, a cooling and/or heating device (30, 40 33) for the cooling or warming of the supply air, and an exhaust air motor (16) which draws the exhaust air from the room (1) to be air-conditioned through an exhaust air channel (11). The desired value (P_{AB SOLL}) for the regulator of the exhaust air motor (16) forms a room excess pressure established with respect to the outside pressure (P_A).