1990 745 GL. 335k mi. Generally runs GREAT. Aces its' emissions test every year.

Now, very occasionally:
-after starting the car and driving,
-then turning it off for a short period and trying to restart, ONLY on warm/hot days
-nothing.

No crank but everything else in/on the dash lights up.

Happened the other day and I grabbed my volt meter and read 12.5 V sitting still.

We used a jump start box and it cranked and fired and ran immediately. Once running we had 13.9V

Now is there some relay or sensor that senses battery voltage to test if it is high enough before engaging the starter?

This car (years and years ago) had a time the key had been on for an hour or so for the radio. Tried to start then and no crank but a jump started immediately.

Back to the first question, what relays/sensors are between the key and the starter that might be ultra sensitive to heat and voltage?

Thanks in advance
Brent
brentcd@gmail.com