Funny how electrons lose their collective minds when overheated!
The fiddler is correct, if you have poor connections you will lose the current you need to produce the work required to move the metal.
Having suffered with similar conditions, I recommend that you check the components around the starter relative to the very HOT exhaust manifold.
There may be connections at the starter that have been corroded, are electromagnetically compromised, or just gunky that when HOT, confuse the path of much needed electrons.
Clean with electronic solvent, tighten, and make sure you have solid wiring.
Some models need a heat shield between them. I think they all should have, but, GM had to turn a profit, right?