My friend, please go back to whatever sources you utilized to come up with this post and re-read them carefully.
In Florida, the vast majority of state correctional facilities are operated by the FDOC and relatively few Florida prisons are operated by private companies. And of the half dozen or so correctional facilities operated by private companies, none of them built or own the facility. It's also worth point our Florida's Bureau of Private Prison Monitoring is responsible for entering into contracts for the design, construction, and operation of privately operated correctional facilities. So, if there's no AC in a Florida prison (and like 3/4 of them don't have AC), whether privately operated or run by the FDOC, your gripe should be with the State of Florida, not the prison operator.
There may be legitimate gripes against private prisons, but lack of air conditioning definitely isn't one of them.
My $.02: the bigger issue with prisons in this country is the fact we imprison so many people over some BS like drugs. Let's make sure we're only putting actual criminal a$$holes in prison. At that point, as far as their treatment, once it's all rapists, murderers, stick-up men, and fraudsters ******** people out of their pensions and 401Ks, I may consider spending my Saturdays under an umbrella with a cooler drinking cold beers as close as I can get to the rec yard while those POS struggle with the heat.