Tenant Rant

A. Make the control inaccessible.
B. Tell him to cough up the approximate difference each month.

If he doesn't like it or wants you to be able to prove what they use, then add a meter and charge for over what you two agree is reasonable for both of you.
If he doesn't like that tell him to GTFO because you are not going to be financially responsible for their financially irresponsible.

Cut and dried and just the way it is, and if you are too nice of a guy to tell him I'll do it as your temp property manager.:D