An integrated system for heating, cooling and compressed air energy storage (CAES) is analyzed from a thermodynamic point of view. The system is based on asynchronous air compression and expansion, in order to take advantage from the daily ambient temperature oscillations and energy cost variations. The analysis is intentionally kept on a fundamental level, without explicit reference to specific components, in order to enlarge the choice of potential applications. Effects of losses in compressor, expander and heat exchangers, as well as heat transfer in the CAES, are included. The proposed system, once optimized and experimentally validated, could become viable options in the wide arena of demand-side energy management.