Whg. Kündigung - leaving early, warm oder kaltmiete?

Hello guys, I gave my 3 month notice at the beginning of last month (1. August) and everything is over at the end of October but I want to leave earlier, I am leaving on 20 September since I have signed the new contract already. The owner of my apartment will not let me suggest anyone (or search himself) to rent this apartment so I do not have to pay double rent and that is okay but since I am leaving early, I asked him if I can only pay kaltmiete since I will register at my new address this month and he will not have to pay for müll and I will not use the apartment at all, so no cold or warm water, no basement usage, no lights outside, and so on, but he is saying I have to pay warmrent and I can stay till the end of October. This is a private house and the owner lives also here. I am not sure but I think the water for my apartment is not measured separately. What are my options? Thanks