No idea about having it in an Audi.
Mk5 golfs had them in.
A good starting point; presumably the air-con system would be very similar?
The A4 B7s can fridges in their glove box.
I think its a whole new glove box though.
http://www.audi-sport.net/vb/audi-s4-a4-a4-cab-b7-chassis/187809-chilled-glove-box.html
It was crap in the B6/7, I had it in my S4 & it was useless, didn't get cold enough tbh on most journeys if at all & of course needed aircon on low all the time, it was another glovebox with a fridge insert part, all it had was a hole in the side of glovebox with a link tube to the heater system, as per web link above.
Best option for chilled stuff in the car is the 12v cooler box for boot etc.
I wouldn't suggest anyone retrofits it in any car intended for.