On something like this, I would wonder what codes it has, and if the CEL isn't on. There are probably codes stored, even if the CEL isn't on. I'm wondering if the IAC just isn't sticking, or if there is something else going on, since you mentioned overheating. Could you give a little more info?

That's the problem with diagnosing over the net, you can't actually hear the sound, but I think my first suggestion of a vacuum leak may really be a partially plugged converter.