The air conditioning apparatus comprises a heat source apparatus, an air blower, a damper disposed in each of branch duct to regulate warm air or cool air to be supplied to each of rooms, a room thermostat placed in each of the rooms, a heat load measuring means and a damper control means. The heat load measuring means controls the degree of opening of the dampers through the damper control means on the basis of output signals of an established temperature and the current room temperature from the room thermostats. Further, the capacity of the heat source apparatus and the capacity of the air blower are determined in accordance with the value of the heat load, and the pressure and the temperature of the air in the air duct.