When using consumables consider the purchase or market price?
Assuming you plan to keep both oil and wood in stock, and they both give you the same quality of heating, presumably you should burn whichever will cost less for you to replace. That would be the fuel that will cost less to buy in the future when you buy it.

If you don't have any special knowledge about what prices will do in the future, I think the most neutral position would be to assume they will stay where they are now, so you should burn whichever currently has the lowest market price - oil in your scenario.

Having done that you could if you wanted to sell the wood that you didn't burn, which you say is worth more than the oil, buy the exact quantity of oil that you did burn, and have money left over. That must be better than burning the wood.

I've assumed for simplicity that there are no transaction costs incurred in the act of buying and selling.