The most likely thing is a credit for federal excise tax paid on the
fuel. Most of the other credits seem related to the purchase of the
heating equipment itself (not fuel), production of biomass fuels, or use
in a trade or business (not residential).
There does not appear to be one single IRS pub or table which lays this
all out, but I'd love to learn otherwise. Compounding the murkiness is
that certain credits have come and gone and come back again over the
last few years with each major new tax law, it seems.
And of course your state may have its own credits. Did your oil company
at least specify whether or not it was a federal credit?