The heated seats were a recall item. I'm not sure if it still applies or in your case. Just tell them it was overheating and no longer works. The overheating and failure was the recall.
If not, check the wiring and for any codes. The heated seat is part of the upholstery. The bottom is pretty easy to change but the top is more of a hassle. There's a writeup in the b5 Passat DIY list on how to reupholster the seats, it's the same on yours.
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