[wongarsu]

Finding ways to cool the air down without electricity might be easier. If nights are still cold you can use thermal mass to get a long-term temperature average (kind of like your caverns). The ancient Persians combined that with evaporation cooling to create fridges. There are also specially engineered paints that radiate heat energy in very specific wavelengths that aren't absorbed by the atmosphere, breaking the equilibrium between absorption and emission of IR and cooling the material by a couple degrees.