My 1990 Lumina won't restart until the engine cools

Hi, the problem your having is going to be with the oxygen sensor this only starts working when the car is at running temp so this is when you start getting problems but when the engine and exhaust are cold you will have no problems starting the car.
The oxygen sensor (lambda sensor as its proper name) runs from the exhaust either before or after the catalitic converter if your car has a cat it goes from the exhaust and the other end plugs into an electric connector these are not to expensive to replace and can be done yourself if you have a good mechanical mind to know what your looking for.

Let me know if you need further assistance ok