My 1981 Corvette will cold start, but when I try to restart it, it won't until it cools off.

Sometimes a temp problem like that is the ignition coil.
Hope this helps.

Hey Les , how's it going ? The thing to do would be hook-up a scan tool an see what the ECM is seeing as far as engine temperature data ! Could have a shorted coolant temp. sensor . And when the check engine light is on a trouble code is present an should point you in the right diagnostic path . For some reason the engine computer thinks the engine is hot when it's not. Choosing an Automotive Scan Tool EricTheCarGuy

Possible EGR valve

Check that your cabin air ducting does not have disconnects and verify the fan is blowing air through the cooling condenser coil. Something may have fallen down through the windshield defroster slots and jammed the fan.

Sounds like you might have a faulty ignition switch and ignition lock cylinder.These cars are known for the ignition switches getting hot and then they won't start.

the idle adjustment needs to be performed warm but the mixture screws at or near the base have springs on then they need turned in all the way and backed out 2 turns then when the vehicle is warm the idle screw is near the linkage also with a spring on it if you have a tach in the car it should its a corvette lol turn the screw in or out until the car idles around 750 to 850 rpm it idles up automatically when cold if your choke is set properlythis should get you where you need to be you may need to adjust mixture screws a little the only proper way to do this is with a vacuum box but you will be in the ballpark anyway with the method i gave you

Coolant temperature sensor is bad. Telling computer that the engine is still cold and over fueling as if it were a cold engine.

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

The neutral safety switch is located in the shifter housing.

Here is a link to a good article on this topic, that would beat an explanation from me.

Brian

Yes, it sounds like the NSS is the culprit.

Theres not enough information, sorry cant help you..