I agree with OK-LL. The best bet is going to be having a thermostat that either you control or locks out if not in a certain range. Tenants will not really care if they are overusing the utilities. And agreeing to pay for the overage is fine in theory but you can bet if they get a bill that they went over the limit and now owe X amount of dollars, they will argue with you that it can't be them and it must be because you used it, etc.
We include water in our apartment. So far with the exception of two tenants it hasn't been a problem. One tenant had his family come over and do 6 large garbage bags filled with laundry every weekend. Obviously, it was an issue. The following tenant, would run the bath water like it was a pool for their kid. The water would be running for 2 hours every few days. These same tenants also ran up their heat and electric bills (they were responsible for that utility) to the point where they owe and still owe the utility company over $1200 on two different accounts (they would put a family member's name on the account instead of paying it off and leaving a deposit).