Have to wait to start

Sounds like a relay or coil.
You'll need to find out if it is not getting spark or fuel pressure when it fails to start.

next time it stops,just take the fuel cap off briefly,then see if it will restart.removing the cap,lets air in,in case the fuel tank is not being vented,creating a vacuum,when motor uses fuel.if that doesnt work,try another ignition coil

Had the same problem with my tracker. Replaced the camshaft position sensor(easy to do yourself, takes about five mins.) Now can drive at highway speeds for about a half hour and stop at the gas station and she'll start back up and run fine. Before i had to wait at least 15-20mins before she would start. Also, if your service engine soon light is on take it to the national chain auto parts stores and they will hook up the code reader for free. The sensor runs about $120.

Presurize system with radiator cap on to see if you are holding 10 to 13 LB pressure as high as 17 LB. Get new radiator cap for your radiator. Check for a slow leak at pump hose thermostat conection , is it wet ?
Do you have a Summer Thermostat ?
Vitally

possible ignition coil pack breaking down...unit cools off them fires plugs again...fuel pressure is a concern also ..possible failing fuel pump

You are more than likely correct about the coil pack.  A lot of times, especially in warmer weather, this happens as coil packs start to go bad.  What happens, is as they start to fail, they get too hot and won't function properly so when you are waiting 20 to get the car started again it is giving it time to cool back down.  Take it to your local auto parts store and let them test it.  That should be your problem and will be an easy fix for you.  Good job with the diagnosis.  Thanks for rating my response and for using FixYa!

have your ignition coil checked, this problem happens when your ignition coil becomes hot and when you rest it cools down and it will work again. you don't repair ignition coil, instead you replace it with a new one.

What engine?

Hi. this sounds like a foulty fuel pump ,,,Check fuel presure when hot .....Good Luck

I have a '81 Firebired that did the same thing with the factory-issued Flintstone-mobile 3.8L V6. Everything but the starter worked correctly: new 185 thermostat, perfect 50-50 coolant misture, no leaks, etc., but still had to wait 1-2 hours for a cool down.

It may be that your original starter is dying. Your starter relay is over-heating and opening the circuit. You can replace the starter and/or buy a pre-made heat shield for the starter or fab one yourself. Regardless, just remember that the goal is to keep the starter as cool as possible.

To prove this is in fact the problem get the engine hotter than usual in your driveway then shut it off. If it won't start cool it down with a bag of ice (don't burn yourself). Should take less than 5 minutes to cool it to start.

Good luck!