Any suggestions to as why after running my 1965 327 Convert Sidepipe car and stopping that the car will not start again til the car cools down. It only happens on hot summer days ??  

Check the thermostat  

Won't start or starter won't crank? [acting like dead batery]  

The condition is called heat soak and is due to engine heat cooking the starter and especially the solenoid. Replace the solenoid with the large original (nonmetric) version, or do what I did a few years ago and get a heavy duty rebuilt (longer body) starter from Oreilly Auto Parts with the larger nonmetric solenoid. It's a cheap fix.