I’m considering a trip in mid-September. Is it usually still too hot, or good conditions, in shadier or higher elevation areas like Black Velvet and Brownstone?
You might get lucky but generally it's still too warm for comfortable climbing. This is coming from someone who's picky about temps and doesn’t climb moderates very often so ymmv. I know some people around here who climb in Red Rock all summer. September is often the prime month for shady routes at Charleston if you're looking for bolt clipping.
I'm one of the guys Earl was talking about who climb through the summer. Just did Chocolate Flakes this weekend on an unseasonably chilly day.
It'll be hot but climbable in the shade if you're not doing 13s. How much fun you have will depend on how tolerant you are of really hot hikes and how much water you're willing to carry.