A supplementary air conditioning system includes an indoor heat exchanger and an outdoor heat exchanger. The indoor heat exchanger is fanless and includes indoor tubes installed so as to be inclined to a ceiling of a room. The indoor tubes make diagonal contact with a high-temperature air zone in an upper part of the room and refrigerant inside the indoor tubes is heated by the air zone so as to boil and vaporize and air in the air zone flows down through the indoor heat exchanger. The external heat exchanger includes outdoor tubes installed outside at a higher position than the indoor tubes and are connected to the indoor tubes via connecting pipes with no compressor therebetween. The outdoor tubes condense and liquefy the refrigerant boiled and vaporized in the indoor tubes and return the refrigerant to the indoor tubes.