Starter heat-soak problems are common. More-common on engines that have headers rather than iron exhaust manifolds.
Two "typical" issues:
1. Corroded wire harness from battery to ignition switch, switch to starter "S" terminal. Low voltage at the "S" terminal doesn't engage the solenoid, which doesn't engage the starter motor. Symptom includes no "click" from solenoid. If you're lucky, you have one location in the harness with a lot of excess resistance. If you're not lucky, you have multiple places each with a little excess resistance. The wire leading to the "S" terminal is usually purple (fades to pink over time) and is often corroded in the final foot before the solenoid--the wire gets road splash from the wheels, or kicked-up by the car ahead. The wire will turn black inside the insulation. (Even the "good" end of this wire is too corroded to save. I had to replace ~3 feet of wire to get to an accessible part of the wire harness that had clean copper.)
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2. Excess heat in the starter/solenoid increases resistance and mechanical drag. The increased resistance reduces current flow, starter may not engage or has little power. Solenoid may or may not "click".
Verify by performing voltage-drop test, and measure amperage on solenoid "S" terminal when key is turned to "Crank". Low voltage indicates wire harness problem, low amperage indicates wire harness or starter solenoid problem.
Measuring the amperage drawn by the starter motor from the main (heavy) battery cable can also yield clues--high amperage indicates a failing starter motor, low amperage indicates excess resistance in the motor windings; or poor contact at the brushes/armature.
There are other possible causes...but these two are each really common.
"Most" folks treat a failing solenoid or a failing motor the same way--they install a "new" or "rebuild" starter/solenoid combination.
A "quick fix" for a corroded wire harness is to install a "Ford Solenoid" on the fender. There's instructions and even "kits" available on the Internet. However, this does not work well with the Permanent Magnet Gear Reduction (PMGR) "Mini-Starters". Mini-starters tend to not disengage properly when used with the "Ford Solenoid" modification.