There are legal limits above which you are allowed to withhold rent. I do not know them by heart since I live in a sunny but colder region of Germany.
So at some point the owner has to take measures to lower the temperature. Be it by installing better insulation or by installing AC. Also: you only have to prove it’s too warm, the owner would need to prove you yourself are causing the heat, if they want to curb paying.
After consulting the Grüneberg, you seem to be right. That is probably just a matter of time though. The Germam High court is notorously pro renter and climate change will also make these matters only worse.