Liability for material defects

Hello together! I bought an A3 8P 2.0 FSI from a used car dealer. Now it turned out that if the car gets warm, e.g. after a motorway ride, it switches bad in the first gears afterwards.(Automatics) I then made this complaint to the dealer. He now offers me 500€ discount, which will probably not be enough for a repair! Alternatively he would take the car back too. However, since I would rather drive the car, and I also on a car. I am rejected, (old vehicle served as a deposit, TÜV now expired), I wonder if he can just do it like that, or if he has to improve due to the lack of material liability?! It would be a great help if someone could answer this question to me!