No one has mentioned this yet but if you know the utility provider (e.g. Eversource, National grid) you can call them and ask them to give you an average of the cost per month in the previous year. They will also be able to tell you summer vs winter. However it doesn't tell you the usage of the previous tenants, so you might use more/less than them and get a very different bill. Not sure about oil heat but did this for my electric and gas bill.