I have an '85 760 GLE with the 6 cylinder engine and some 320K miles
Normally, the car starts up just fine. However, after the car has run for a few minutes, if you turn it off and try to start it again, it will sometimes not start. When you turn the ignition, all the lights come on on the dash, but the car makes no attempt to turn over. After it sits for some period of time, it sill then start up just fine. It appears to be heat related and will only start after whichever part has cooled.

Does anyone have any insigt into just which part(s) might be causing this behavior: warming up not interfering with the running of the car but preventing it from turning over when the ignition is turned. TIA.

 

This must be the longest living 760 PRV-- You must be doing something right!
I'd look at the starter; being an electric motor, as it heats up it may act up...
The Neutral Safety Switch is another candidate to look at--have seen this happen on other cars...

 

I inherited it from my parents kind of ... my dad treated his Volvo's right, dealer service at all the prescribed intervals. It has a number of little electronic annoyances, but mechanically and the body just keep on truckin'. Ya gotta love a pre-Ford Volvo.

Thanks for the insight, I will look into those things.