An air conditioning system for cooling or heating an air, and for feeding the heated or cooled air to predetermined portions is characterized by comprising: a first circulating circuit for circulating a first heating medium; a second circulating circuit for circulating a second heating medium; a control unit for controlling the heat for executing heat exchange between the first heating medium and the second heating medium to flow through either the heat exchanger or the first heat storing device. Moreover, an air temperature is controlled by heat of the second heating medium.