The temperature swing can be much greater than 100 C. Heat can be extracted as a wave passing through the store, then heat added back by reversing the flow. It would operate like a counterflow heat exchanger.
View another way: if we hook several piles in series, then lukewarm air from a first mostly discharged pile can be directed into later piles for more heating. In the continuous limit this is the concept I described above.
View another way: if we hook several piles in series, then lukewarm air from a first mostly discharged pile can be directed into later piles for more heating. In the continuous limit this is the concept I described above.