A method is disclosed for supplying air conditioned air to a residence or building interior. The method entails positioning a heat and mass exchanger to discharge conditioned air into the residence or building interior. Further, a rotatable desiccant wheel dehumidifier in positioned in fluid communication with the h 5 eat and mass exchanger. Supply air is received and treated in the dehumidifier, thereby supplying dry air to the heat and mass exchanger and exhausting hot humid air. The heat and mass exchanger is positioned and configured to received dry air from the dehumidifier and supply cooler dry air to the residence or building interior, or other target environment. A system is also disclosed for operating the described air supplying or air conditioning method.