To ensure cooling of indoor air in the case where there are successive tropical nights, in a system for cooling indoor air of a building by using a heat exchanging method which employs a heat storage material.

A large quantity of water to be used as a heat storage material is stored in a reserve tank 3 which is provided underground. Water is thus cooled by the ground heat. Then, a portion of the water stored in the reserve tank 3 is taken out therefrom and supplied to a heat exchanging tank 4 having a small capacity, followed by sending air to a ventilation pipe 10 which is furnished in the heat exchanging tank 4 in a immersed condition. Thus sent air is discharged to the inside of a building 2 through a supply air duct 15 to lower indoor temperature. Since the reserve tank 3 has a large capacity, and therefore, the water therein is maintained cool by the ground heat during heat exchange, water having a given temperature can be constantly supplied to the heat exchanging tank 4, thereby realizing a continuous use.