Hi Mead
First, next time it won't start, try this: press the accelerator all the way down and keep it there. Then there'll be no vacuum so the engine cannot draw fuel from the carb. After a few seconds the intake will have cleared of any fuel and the car will probably start, keep the pedal down until it hits e.g. 2000 rpm, then release quickly, don't want to overrev it.
If this procedure works, that confirms that you have too rich carb situation, which the engine likes when cold, but not when hot. Float valve is a possibility, but idle screws, choke and broken/hardened power valve are other possibilities. I'd recommend a full tune of your carb as described on:
http://www.tuningmadeeasy.com/...a-carburetor-part-1/
Feel free to pm me if anything is unclear, remember I'm GMT+2
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