The tenant has a thermostat, run it up a couple points.You obviously don't have real world experience, so please!!!!

One trick, and a good idea anyway if it's not already set up this way, is to have a thermostatic mixing valve on the output of the heater and have the heater set to it's max temp.

They'll whine when you tell them they can't set the thermostat to 80 in the middle of the winter.

One way is to install a thermostat that reminds the tenants to replace the filter.

The tenant might want a pet, or central air, or a setback thermostat, or a ceiling fan,  or some appliance.

Can I install a furnace guard (lock) on the thermostat since it is in MY NAME??

do they make electric baseboard heaters that allow a wall mounted thermostat or do most of them have the thermostat directly on the unit?  

There are thermostats you can put in that limit the heat from between 68-72, so the tenants don't crank it up.

It is gas, and I've replaced a few things on it - the combustion fan, the gas valve, thermostat, and the ignitor (twice) - but otherwise it just keeps plugging away.

I'd make appointment and go in and see the temp on the thermostat in her apartment.If your other residents are using portable heaters I'd not let them, huge fire hazard,, electrical fires., I have a clause in my lease no other heat sources permitted, Is it forced air or radiators, your post only said type of fuel used, if it's radiators, go in make sure all radiators are system ready that they are full of water and no air locks,, YOU TUBE it to figure out how to do it.