I'd recommend a diagnostic check to see if any fault codes flag up. If you take it to Audi I'd expect to see some form of good will on the repair despite being out of warranty
It is a very common issue on vag cars as well as other manufacturers. My wife has a jaguar xe and it's also known for faults. Hence why in our case we get Jag tecs to fill the adblue tank up when it need it with genuine adblue. That way they can't blame us for over filling it or putting wrong fluid in it etc. It has saved us expensive bills twice when the system has gone wrong and Jag have had to drain the tank and reset the system FOC. Even though the car is well out of warranty.
How long have you had the car? And was it a private or trade sale?
It might be worth you speaking to a retrofitted like autologics as it sounds like the climate system hasn't been fitted quite right.
I'd recommend a stainless steel straight through exhaust, induction kit and then the remap. Obviously you could look at upgraded cams, manifolds etc but is it worth it?
Welcome to the forum you'll find the members on here are a friendly and helpful bunch 🙂 I agree with Gareth's advice. The other thing you could do is get a diagnostic check to see if any fault codes flag up.
Is it a remap on a rolling road?
Have a look at Celtic tuning website as they show you what gains you can get from their maps which you could use for reference.
You might need to also consider a remap on the gearbox.