First Duplex-One Furnace. How to navigate?

[Kyle Galloway]

My partner and I are finishing up a duplex. It has one furnace and one thermostat in the down unit that controls the temperature for the entire house-both units. My plan is to get a lock box installed around the thermostat so the tenants cannot adjust it once we agree on a temp so only I have access. My question-how do I navigate the billing and rents? The bill for the furnace will likely end up on the gas bill for the lower 2 bdr unit. This will give a huge discount for the 1 bdr upper unit and obviously a huge liability to the downstairs. I have looked in to installing an upstairs furnace and separating but it is not economical. My thoughts:

Communicate and be transparent with the tenants for both units and explain the situation-I.E. the downstairs tenant is essentially paying for the heat of the upstairs. I would then give a "discount" of say $75/month for the downstairs unit-the unit paying for the heat-and an offsetting "charge" of $75 to the upper unit. This $ amount can be adjusted when I do the research with the utility company on historical costs-assuming I can-but that is the concept. Also the lockbox so the downstairs tenant cannot alter the temp for the upper unit. I control it all and list the temp in the lease potentially. Does 69 degrees sound reasonable? That is what I keep my own house. 

Do you guys think this is fair? Do you believe the tenants will think this is fair? Thoughts or ideas?