Hi Shawn
I have a Q8 55 TFSI bought from new in September 2020. So just over 2 years old. Also I reside in the U.K. and we don't very often suffer from very high temperatures here !
My brakes can squeak a bit, especially so when I haven't used the car for a few days, but not to the extent of the problem you are suffering I suspect.
My wife and I are currently in the car in Deutschland touring. In the last 3 weeks we have covered almost 2,500 miles, driving from Calais France south to the Bavarian Alps in Berchtesgaden and then north again to Lower Saxony where we are staying at the moment.
Half of those miles have beeen on the German Autobahns, many of them without any speed restrictions at all so average speeds can exceed over 100 mph. I will just say that the Q8 has performed superbly, mixing with the best that Germany can offer ! I think the car attracts a bit because they are still a very rare car in Germany....and perhaps the British number plate and U.K. sticker on the back is sometimes like a red rag to a bull to the odd few German motorists !
Regarding your particular problems re brakes.....mine have performed superbly with no squeaks and very little brake fade, even powering down quite rapidly from very high speeds on the Autobahn.
So, my 2 penneth is that your Dealership is quite wrong regards the reason why you have brake noise and my advice is to pursue them further until they sort it out. Possibly a fit of new pads all round should be requested.
Hope this helps a bit....and enjoy this wonderful car of ours.
Frank