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Check the spark plug caps . Dusty
This is interesting. An idling motor doesn't generate much heat so I guess it would depend on ambient temp to know just how hot things got. Likely the enrichening circuit might have just loaded the plug. Best change the oil that's for sure.
How much gas is left in the tank...sounds like you might have just run out of gas perhaps.
I typically take the bike in the shower with me, but that's just me.