The melting of your thrust pad was caused by friction...ie. the clutch cone rubbing hard up against the plastic.
And no, I have never had a reason to put my fingers on the clutch cone after mowing, engine stopped of course...but I should imagine it would get warm but not hot enough to melt plastic unless something was drastically wrong.
A word of caution: Do
NOT place you fingers anywhere near the clutch assembly whilst the engine is running.
