I may stop by the property to change a filter, and every light in the house is on, the tenants take hour-long showers, and keep the thermostat wherever they please.

I use it to make sure the temp matches our thermostat.

One unit houses the thermostat for the furnace which heats the whole building.

Is it legal to put a lock box on the thermostat?

When we switched over to auto-set back, limiting thermostats I had a tenant call me and ask why he couldn't get the thermostat up to 80 degrees (max 71).

Each unit has it own separate gas mete, gas bills, heaters and water tanks also separate thermostats also.

Amazon.com: Happybuy Coin Operated Timer Control Power Supply Box Coin Acceptor Programmable Control Coin Acceptor Multi Coin Selector for Vending Machine Electronicial Device, 110V: Industrial & ScientificLearning to program it is a little more complicated than I expected. 

I am not a fan or keypad locks, Ring doorbells, Nest thermostats or other technology in long term rentals. 

They are very efficient means of heating space, so long as your tenants aren't leaving windows open as their "thermostat".

The 2nd floor apt is fabulous, I have a very responsible tenant that wants to move in (she can pay 1300. but that's all) The thermostat is in her apt so I need someone responsible there.