The system comprises an air delivery motor (15) which feeds the air via an air delivery channel (10) to the room (1) which is to be air conditioned. The air delivery channel contains a heating and-or cooling device (30,40,3) for cooling or heating the air and an extraction motor (16). The extraction motor sucks the air out of the room via an extraction channel (11). The demand value for the extraction motor controller forms a fixed room overpressure compared to the external pressure.