The location of the Pontiac engine starter has always be problem on my 79 TA. After spending years restoring the car to be mostly a show car, I attended a car show in the early part of this year (2022) and drove 12 miles to the venue. I parked and then was immediately asked to move the car to a different spot. I hopped in the car and "nothing." No start, no engine turn over...nothing. The car looked like a million bucks but would not start. I live in South Florida so, it's alway 80 degrees and the engine temperature was only 185. Luckily I was able to jump it with a portable "sparky" I took with me on this outing. After the show, the car started right up and I drove the car home. I pulled into the garage and shut the engine off and sat there for a minute and could not start up the engine. I believed it was heat soak. Annoyed as hell because of the expensive Jet Hot ceramic coating on my headers to protect high heat, I decided to get shielding to wrap my starter. In addition, I decided to replace the battery cable and battery. I purchased these items and installed each of them. BINGO all good again. I have a conventional starter by the way.
The bottom line: If you have a new starter, new battery, quality headers in place and the beast doesn't want to start after running at normal temperature, it's probably bad electrical wiring. In my case, the wiring to the starter was 43 years old!