2016 Jazz Blue A8 Scat
If the injectors haven't been changed it's probably not this issue.This sounds like what is wrong with my tune. It hunts for idle when hot, but no issues with starting hot. My mods are simple - CAI, Fastman throttle, Catback, and 180 t-stat. I get 434whp and 436wtq in my 2011 392 A5. 12.369 @ 112mph best time on stock Goodyear 255/45/20 junk.
The car was tuned on a cold day (40). The place I got it tuned is long out of business. I guess there isn't a way to fix this if all I have is a Trinity (which he used just to upload the tune).
For the most part it runs fine. When it is stuck in traffic and getting hot, the idle will surge. Gets exciting if my foot isn't on the brake. I chalk it up to the car being mad because it wants to GO.
It's hard to say what's wrong with it without being able to see the tune. I doubt there is much to be gained from a tune with your short mod list so I'd try throwing a stock tune back in and see how it runs.
It could be related to the larger throttle body.