i recently fixed my GMC won't start hot because the coil was on the edge of going bad, it wouldn't spark good enough to hot start, but cold it would
these engines get hot fast, maybe your coil is warming up and can't spark no more
but do as other suggested, check fuel delivery first
A / B testing a new coil isn't too difficult after than
it's probably not the carburetor if it can run for 12 minutes
-s
