My gov't profile guns' POI don't change whether they're hot or not.
POI will change, however, with a pencil barrel when subjected to long strings of fire. I usually see some vertical stringing in the 3-4 inch range once the barrel gets heated up. Practically speaking, this is of little concern.
Note: I suppose it's within the realm of possibility that you'd have to run the gun hard for a couple magazines (e.g. a "break contact" situation) then almost immediately be pressed into having to take single precision shot at range, but this is about the only scenario I can fathom where a pencil barrel would prove to be a hindrance.
FWIW
"On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died." -Adlai E. Stevenson II
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