The temperature would be at 50 degrees, I would kick on the heat when I leave my house, and the rental would be warm by the time I arrived.Then one day I was doing some work and noticed the fan was running constantly.

Just a simple unit where you have to be present to push the button and set the temperature will be just fine for them.

I've heard of thermostats that only allow temperatures within a certain range or that have useful Wi-Fi components for managing utility usage.

Hello, I have a 3 unit property, and I pay the heating on the property I do want to upgrade the thermostat before the colder weather which is recommended heat only I have radiant heat I looking for thermostat that I can lock the temperature tenants cannot raise the temperature.

I haven't had a problem despite the area experiencing temperatures down to zero. 

You can create a rule that says if the indoor temperature reaches “x” degrees, then turn the heat on, AC off, etc. 

@Sarah Kensinger If you guys have a back to back turn over and change your entire water, how do you ensure it is heated all the way back up to temperature before the next guest arrives?

My suspicion is that if your temperature is at or near 98.6 degrees- you qualify.

Quote from @Dustin Sanders: @Quinn Olivarez I have the 3 markets I'm in listed below:- Pensacola, FL- St Petersburg, FL (technically Gulfport, FL)- Helen, GA I would think Helen GA will pick up when the temperature warms up.

@Zach Wright yes i agree that can be quite a worry. you may want to look into lockable thermostats. i have thermostats that are locked at a certain temperature and cannot be changed without a code.each city/state has laws on what that temp needs to be, but maybe this is an option for you.