To this day I ask her what "off" means on the thermostat.

Also, if you have some kind of green energy saving thermostat that micro manages the temperature throughout the day, that might be an issue.An old school Honeywell with no adjustments might be worth a try.Even a low IQ renter should be able to handle these.

If so, put a new thermostat in the tenants unit with wifi capabilities and connect it to your device.

I asked her to change the filters and double check the thermostats (there's independent upstairs and downstairs controls) and get back to me if it's not better.But how would you all proceed??

I also could (do not yet) have controllers on the thermostat, lights, etc.

Ideally I would (if I buy it) put in two gas meters but if that's not practical, is there a thermostat that is set at 70 deg but the tenant can turn it off or on but not adjust the temperature?

I don’t want to include utilities in rent because they would have no incentive to be conservative with thermostat.

Another thing is use is an air freshening system that we can use remotely, same access sort of deal with out thermostat. 

Everything working as It should.Tenant not satisfied says It only is 62 in apartment and thermostat is at 76. 

In other words, let's say over the winter the cost of oil to heat tenants who don't care if the thermostat is left on at 80 degrees with the window open - runs $300/month.