A method of cooling moist air through a heat exchange surface suppresses the formation of dew and frost on a heat exchange surface by preparing a carrier which has a heat conduction ratio higher than that of the moist air if the air temperature in a temperature boundary layer, is below the dew-point when the air temperature in the temperature boundary layer is above 0° C., or below the freezing-point when the air temperature in the temperature boundary layer is below 0° C., the carrier being arranged within the temperature boundary layer and on the heat exchange surface, which is in contact with moist air and is used for cooling; and removing moisture from the air by condensing or sublimating water vapor in the moist air on the surface of the carrier by arranging the carrier opposite of the heat exchange surface and within the temperature boundary layer.