Those citizens "making do" generally have freedom of movement, free access to cool water, air-conditioned businesses or vehicles, and are not locked down in a concrete facility.
There is a absolutely no nuance to this.
Sweat is a wet-bulb cooling process which always cools below ambient for any humidity less than 100%.
Over ~95 degrees, a fan blowing on a human acts as a convection oven, increasing body temperature while dehydrating the body.
This is greatly exacerbated in extreme heat.
CDC guidance is to avoid using a fan in extreme heat conditions unless it is combined with a cooling source and careful hydration. Once again, not exactly an option in a Texas prison.
The reason humans do not drop dead when they go outside in >100 degree weather is because sweat evaporates and lowers the temperature of humans skin below the temperature of the air: sweating skin is wet-bulb temperature and the reading on a thermometer is dry bulb temperature. This is dependent on hydration and evaporation, which is why you must hydrate and wear breathable clothing in order to avoid heat stroke, and it is why high ambient humidity is more dangerous.
https://en.wikipedia.org/wiki/Wet-bulb_temperature
You don't want to put a fan in your face, but gentle circulation of air helps to aid evaporation. Have you felt the difference between stagnant air and a gentle breeze on a hot day? As you sweat, the air immediately around you absorbs the water from your skin and increases in humidity. Gentle circulation helps to move this higher humidity air away from your skin and replace it with dryer air that has a greater capacity to evaporate more water and therefore remove more heat from your skin.
The prevalence of air conditioning is a very recent thing and for most of human existence on earth people survived in hot areas by taking advantage of evaporative cooling.
That, of course, doesn't mean we should treat prisoners poorly. But we don't need to misrepresent the science.
ambient and body temperature arent coupled items there
have you never used a convection oven?
Yeah. A one-shot investment of 10k$ per prisoner to avoid more manslaughter cases is peanuts, really.
The former almost certainly includes other installation part, utility, and labor costs. Even if you could give everyone a $200 window unit, you'd need to deliver, install, upgrade utilities, maintain them, etc.
Some times people walk into supermarkets just to cool down.