Is the prohibition of other heat sources in district heating lawful?

It is the municipal utilities that write, if you continue to use our district heating, then only this and nothing else? We wonder whether this is lawful?

In principle, both a connection obligation and a usage obligation (= no other heating) are possible for district heating. Whether the respective local statutes are legally compliant must be decided by a specialist lawyer.

Basically, with district heating, both a connection obligation and a usage obligation (= no other heating) are possible. Whether the corresponding local regulations are all legally secure must be decided by a specialist lawyer.

Does that mean I am not allowed to operate a fireplace?

Provided that the obligation to use is legally secure, yes. The wording "the entire heat" is also likely to exclude additional heaters such as the fireplace. One question now, for example, is whether it is lawful to introduce such an obligation to use by contract with one month's prior notice and whether the district heating provider is even authorized to compel someone to such an agreement. Or whether this must be decided by the municipal council through a statute, with transitional periods. As a legal layperson, I am out of my depth here.

You do have a valid contract. The letter is a unilateral declaration of intent, but I would definitely consult a lawyer about that.

we have been living in our house for 7 years, use district heating from the municipal utilities and have a wood-burning stove.
[ / ] The house is now 7 years old. And we were the builders ourselves. [ / ] If I do not sign the contract, it will get cold in the house from then on. It is practically a dilemma.

As first occupants and builders, you know whether there was a connection and usage obligation in the development plan – since a heating appliance was approved for you, apparently not. Any interim changes to the development plan have no effect on existing buildings, but possibly on their conversions. I also cannot imagine a different municipal statute with retroactive intervention being lawful. If such has nevertheless occurred, the lawyer will probably advise a constitutional complaint. Regarding the supply contract, I could imagine that he would advise concluding it with the clause deleted. I do not see the dilemma in two ways: firstly, you mention a wood-burning stove (which you could logically also use without this prohibitive contract), and secondly, I only know the principle that a local supplier must step in with a basic supply tariff if the contractual supplier fails. Coercion and extortion are criminal offenses, and I certainly do not see the threat of a significant disadvantage as far removed from that. A forum can only be a first sounding board; going to a lawyer seems appropriate here. There is still plenty of time for the lawyer to send mail to the supplier.

What is written in the land register? Something like that is included in our land register.

That would be disproportionate and the wrong instrument according to my legal understanding. Except if the municipality was the seller of the property and the condition was in the purchase contract. In some municipal councils, environmentalism drives worrying excesses. Climate goals may be legitimate, but property and its reasonable use are so as well.

The question of whether it is a statutory district for district heating and whether there is a connection and user obligation was not clearly answered by the questioner.

All advice is therefore speculation.

Hence, please provide a clarification first.