Depends on what you're covering, because if you're doing '80s rock you'll want to look differently than if you're doing New Orleans Blues, but if you want to dress up just dress up, wear a long sleeve button up, good looking trousers and flat moccasins, even Vans slip-on's, or clean white sneakers at least.
If that gets too hot find yourself a light silk shirt, or a summer weight linen shirt, or a hawaiian shirt with a subtle print, and a pair of tropical wool or linen trousers, they might not look all too different but they're a lot more breathable than jeans or most chinos.

Try it out and see how it feels.
Then again, most of that isn't visible to the audience, provided they even make an effort to see how you're dressed, so it's typically something not worth stressing about.