My tenant paid half of the rent and we split the heating bill . Now we ran out of oil and they want me to pay for all of the oil even though they chose to pay half of the heat and they signed the lease stating they understood they were responsible to pay half of the heat. If anyone knows what I might be able to do please let me know.

Depending on where you are, heating may not be an issue in a few days... you need to write your lease so that the oil bill needs to be paid within 5 days of your billing OR the unpaid charge will become due and payable as rent so this way you can take the oil payment for their next monies, leave a balance due on the rent and evict them...

Heating oil should not go below 20% in the tank so keeping it on automatic fill with the fuel oil provider is the BEST way to insure the heat stays on and the bill is paid.

Did you have two types of heat? You said you were splitting the heating bill. So was there another heating bill over the oil? I ask since when I heated with oil that was our heat bill?