I was told by a local body shop that chroming (or powder coating) my valve covers will build up heat and therefore decrease performance. I guess polishing is the only way to go?

The vale covers on the 2005/06 Mustang GT are made of
magnesium. the chroming process and magnesium do not mix well.

I've never heard of a heat issue with powder or paint on valve covers. On cylinder heads or engine blocks this can cause major problems though.

I doubt it is even a measurable performance difference. All kinds of manufacturers have been making and still make powder coated cam/valve covers. Even the Ford GT's covers are factory powder coated, and Ford Racing sells a variety of powder coated cam covers for the Mustang GT.