I'm sort of thinking out loud here but could you have two batteries running simultaneously but on opposite cycles, so while one is cooling the other is heating? Obviously it wouldn't be 100% efficient but it might reduce some wasted energy.
The heat and cold are created by the compressing or decompressing the CO2 (our any other gas). If one battery is heating while the other needs heat that would imply that one is charging while the other discharges, which is rarely useful in normal operation
