My 2013 Audi TT interior caught fire this week, and I found this thread. Worryingly I'd been complaining to Audi about a burning smell in the car, they had it in and changed a DPF bracket underneath, but when I explained I didn't think an exhaust issue was the problem as it was a plastic burning smell from INSIDE the car, they gave me the car back and advised me to continue and see how I got on with it. That same evening driving it home from the dealer I could smell the burning again...I immediately telephoned the dealer but all service department had gone home as it was after 6pm. I advised a chap whom answered my call that I would be returning the car first thing the next morning. Next morning came, it was frosty so I had all the heaters on and windscreen defrosts etc. as one would expect, and 10-15 minutes into my drive smoke came out of the vents and nasty fumes filled the cabin, I pulled over when safe to do so (and as quickly as I could) and got out and proceeded to ring Audi Assist. As I was giving my details I saw the car burst into flames from the right hand side dashboard area, the next thing I knew I'm awaiting the fire brigade who quickly arrived in minutes and put out and made the car safe. the whole of the right side of the dash next to the steering wheel and light switches was melted away and lots of wires visibly burning red hot. The fire brigade said it was in their opinion definitely an electrical fire.
My supplying Audi dealer have been very supportive (so far) but I'm yet to hear from anyone at Audi UK, even to apologise etc... I was having nothing but trouble with the car prior to this with parts falling off it and annoying rattles to name but a few issues.
I hope judging by this thread I don't suffer the same fate, its not looking promising for me after reading here though :(