My 1983 oldsmobile delta 88 runs til it heats up. Then it stalls out and won't start til it cools off. What could it be?

When it stalls out, if it cranks good but won't start, have a helper crank it while you visually check for spark at the spark plugs. A spark tester from the auto store doesn't cost much, you can carry it in your glove box. If the engine is hot, wear gloves.

With temp issues check the coolant temp sensor. How long since a tune-up, I'd also want to check fuel pressure. Check for applicable trouble codes. Your obd1, you should be able to check codes, yourself. You use a jumper wire between the A & B terminals at the data link connector, usually lower edge of dash between steering column and driver door. Turn key just till the dash lights come on, no further. The mil on the dash starts flashing, you count the flashes to get the codes. Your looking for two digit codes.