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. 

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.  

Before you do that, install some passive roof vents or an attic exhaust fan on a thermostat switch with a passive intake on the other side of the attic.  

I have to agree with @Roy N.. i provide free Internet myself to my student rentals ( i also control the thermostat and door locks if i have to, from my house - which includes changing the door code with new students, front door only) its a convenience for them and me and helps rent it. as for my other properties i do not provide that service, the tenants pay for that service themselves.

Even as a precaution, the thermostats for the heat are programmed not to exceed certain temperatures, so that is controlled to an extent as well.