I should have money back
If the heating account show that you have paid too much on account, it is because you have had a usage less than your payment on account. In such a case, your apartment administrator is responsible for the payout.
More than likely, you will receive your back payment together with the first charge of rent after you have received the consumption account. The landlord can deduct the amount from your rent, so the rent becomes lower in the given month.
These answers are based on the current situation in Denmark, and may vary by country. If this wasn't the answer you were looking for, please feel free to contact us.