Andy,
My GTI did the same thing when it got older. The issue had me worried, but it turned out to be something simple. There are several thin pieces of steel that cover portions of your exhaust system. The piece that covered my catalytic convertor came loose at one of the welds. the shuttering was worse when it was cold because of metal was "shrunken" and would rattle off of the CC. When it warmed, the metal expanded and allowed enough room that the piece didn't hit the CC. I think that may be you problem also.
Art