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OP have an electrician out to look at the power. Basement should have its own circuits that can be run through a sub-meter. You can set the rent to include x amount of electricity and they pay for overage.
If it is gas heat, remove the thermostat control completely from the basement. Put a remote sensor in the apartment for the thermostat to read the temperature but the actual control unit is where the tenant can't access it. Rental agreement will say that heat is provided to x degrees... be reasonable, say heat is provided up to 72 degrees. If tenants want more, they can use oil filled radiators which will be on their electric bill
Then you also have to worry about the tenant using the stove for heat. So have an electric stove. They pay for excess electric heat so running the oven for heat won't be free and won't kill anyone with carbon monoxide.
Having experimented with different models etc, I would say get the most simple basic one you can find. The fancy programmable ones are a PIA that seem to need constant attention and reading of very small printing.