Tenant Rant

Put a few bucks out and move the T-Stat, into the lower apartment or shop. Then you will have full control. Putting a lock box on at this stage could be asking for damage to the apartment, when he pulls it of the wall. I don't know anything about US. law, but here in Canada a lease is a binding contract and both parties are obliged to follow its terms. Good luck, no matter what you decide to do.