There's plastic and there's plastic! Bit of a misused word probably.
But no, hard(ish) 'plastics' or whatever the material actually is, won't. Modern (not-bakelite) HT pick-ups don't melt, sliprings don't melt on the inside of the thing, plastic insulators don't melt on the cb unit. A mag body will get hot to the touch, sure, too hot to touch in summer probably, but never seen a meltdown in normal use.!