I am not sure this is helpful but my lumina has heat but it does not work when I am sitting. After I turn a corner it seems to work. It stops when I am parked most of the time but usually resumes after reving up the engine.
I thought it was a broken door valve , letting the door swing from cold to hot air. But since it stops blowing when at idle and starts blowing hot when reved up ?
My chrysler had the same problem with the a/c . It was a broken vacuum valve on the door for the hot and cold air flow.