Get the smart/remote devices and put a lock on them for a certain time/temperature.

The temperature that night got down to 0 degrees farenheit.

What you could do is have it set to a particular temperature with a lock box over the thermostat.  

I realize people have different temperature sensitivities, but still. 

In the process of doing this BRRRR I had to deal with a broken water supply line at 6 am, a roofing contractor that didn't do a good job and left my roof leaking in various spots, and a call from my new tenants saying that the house was flooding because apparently, as we found out later, the plumber didn't weld the copper supply lines to the shower valve correctly and water was coming out from the wall.

I called the installer and they were 2 weeks out because temperatures here are in the 90s-100s right now.

Or, they will develop a box that just sits there and blasts out cold air into a house which will reduce the summer heat to a much more livable temperature.

An under market tenant may not be your biggest problem.I'd recommend easing into landlording and getting your systems in place rather than cleaning house and risking Holiday Season (and winter temperature) vacancies.

A lot of people up north have them but also have a back up supply for heat due to them not working well or efficiently when the temperatures get very cold. 

Climate change is coming for Florida in a big way and between beach erosion, sea level rise, and rising temperatures, I think more people will be looking to vacation north of Florida in the future.