I suspect the engine quitting in the high temperature is a coincidence. Vehicles that sit around not being driven and then suddenly are awakened from their slumber often develop problems they didn't have before.
You will have to do the usual investigation of fuel and ignition parts.
When it conked out and wouldn't start, did you investigate? look down the carb to see if goosing the throttle squirts fuel into the venturi? Disconnect the fuel line at the carb to see if fuel is actually getting to the carb?
After the last conkout, did it eventually restart? How did you get it home? Have you tried to start it since then?
