Hydrostor’s patented A-CAES technology, which Energy-Storage.News recently discussed with company president Jon Norman, uses excess grid electricity to produce heated compressed air. The heat produced during the process is stored above ground and the cool compressed air is forced underground pushing water stored in a cavern into an above-ground reservoir, storing potential energy in the form of compressed air and heat.
When required, the process can be reversed, discharging electricity back onto the grid.
(Comment: I would expect that geothermal energy assists in thermal management. )
See also
World’s first commercial Advanced Compressed Air Energy Storage completed (appro.org)