Inmates in prison even heat sensitive ones has no right to air conditioning or really anything for that matter.
Prison isn't supposed to be comfortable. Prison is supposed to be made the worst place you want to be so you'll avoid going to prison. But some people who've been to prison commit crimes again and wind back up in the prison.
Although I do think at least the prisons should have some air conditioning during the real hot days for at least the guards and other staff that work there.
But to have the cells air conditioned I think a fan should be adequate for the people in the prison cells.
Although I've heard of a few prisons having air conditioner vents in prison cells but they're usually not turned on unless absolutely needed.