Good day
I have a 1990 Trans Am GTA 5speed, 305 TPI.
The problem is after reaching operating temperature (185deg F) and turn the car off, and if the engine temperature raises at or above 200deg F the car will not turn over until the engine temperature drops below 185deg F. When I try to start the car at 200deg F the voltage gage shows 12-13 + volts until I turn the key to start and then it drops below 10 volts. At 200deg F + I can jumpstart it and or push start it with no issues (Starts right up). I replaced the battery (No change)
So before I go nuts and start replacing all kind of stuff like + and - battery cables, starter, and whatever I figured I ask if anyone has seen or had this issue.

 

I would suspect the starter, but before I bought one, I'd pull the old one and look it over for loose bushings/worn brushes/worn commutator, loose or corroded field windings, etc. for the 'smoking gun' indicating that it is the culprit.

Additionally, check all connections, especially grounds, for corrosion and looseness.

 

The first thing to inspect is the large Ground-Cable from the Negative-Post of the Battery to the Cylinder-Block.
If is is loose or damaged...
The Starter-Motor may not have enough Current to start the Engine.
Especially if Electric-Fans are ON at this time.

 

I have seen Vehicles crank and start with the main Ground-Cable disconnected, and the Engine completely cold.
What would happen is...
The smaller Ground-Straps would provide enough Current for the Starter to crank, with a cold Engine and minimal Electric Components on.

Good luck, hopefully it is simple to find and fix.