Well.... that's a good sign.
I was looking for what might have gotten "heat soaked" and then was breaking down. A coil could do that. Carb can as you know. Starter motors can get real cranky (pun) when hot.
I'd go around and check ALL your electrical connections... coil - starter motor etc because HEAT can cause unusually high resistance. And this would be a "just to be sure" measure.
Also -- given the high heat where you live.... do you have a phenolic spacer under the carb?
