Yup... LOL. That's a common one.
I had to learn that lesson a while back too. You are correct with the extra heat part though... at 100+ and at idle, it seems like it's blowing room temp air (hot). Then I put it in neutral and push it up to 3k and now it's nice and cold.

I'm leaning toward the dying compressor idea. But for now, I just try to avoid surface streets. LOL