The most important thing: compare your heating cost statement with the monthly installments you paid - if the final amount is significantly higher, you're entitled to a detailed explanation from your landlord. You can't just ignore the statement, but you're allowed and should question it if it seems unrealistic to you.
Rising energy prices are indeed a legal reason for higher utility costs - that's completely normal. But here's the thing: your landlord has to be able to prove to you that the calculation is correct. Ask to see the detailed statement - how were the costs divided among the individual apartments, what are the heating costs per square meter, do the consumption figures check out? With oil heating, it can also happen that oil delivery rates fluctuate, which drives costs up. That's annoying, but it's legal.
If you have doubts about whether everything is correct, you can hire an accounting expert to review it (might cost 200-400 euros, but the landlord has to pay if the statement turns out to be wrong). Or contact the tenants' association in Munich - they review statements like this for free and can tell you if something's off. A doubling is pretty extreme, but without more detailed information about previous years' prices and your actual consumption, you can't say whether it's unlawful.