I used to live in a small 1-home office apartment, & it had 1 of those battery operated thermostats.
At first, I didn’t realize the thermostat used batteries, but if you saw how old it looked then you would easily guess that it did.
It took the battery running out for myself and others to realize that I needed to change the batteries at least once per year. I remember the day when I came beach apartment & saw that the thermostat was blank. I wanted to call the leasing office, but it was after minutes, so I had to wait until the next day. Anyway, that evening I was dreading having to sleep in my house with no cooling system & I complained to a friend of mine about it. He randomly asked if I checked the batteries in the thermostat. I asked him what he meant, & it was then that I realized that the thermostat used double AA batteries. Once I figured out how to unaffix the thermostat from the wall, I changed the batteries, & the air conditioner was working fine… Fast forward to today, I am not sure if the thermostat that I have uses them or not. I think that it is hardwired to the house, & might have batteries as a means for backup power. I have lived here for over 5 years now & I have never had to change the battery, so who knows if it uses any… But I would love to substitute to a programmable or perhaps a Smart thermostat. I don’t know I would need to worry about needing batteries for them.