As mentioned earlier, many should read my article on heat-treating barrels, recently published RIFLE. Even the tight-contour barrels that so many shooters still believe "walk" due to warming with more than one shot do NOT, because most are correctly stress-relieved these days.
As stated in the article, waiting a while between shoot tends to enlarge groups, for two reasons: You probably won't be holding the rifle in a similar way, and wind conditions have changed. This is exactly why many target shooters rattle off shots during the same "wind conditions."
Also, most "hunderd-yard hunters" (as somebody recently called most handloaders) never put out wind flags. As a result, they have no clue whether the 1st, 2nd or 3rd shot was tripped off during different "wind conditions," which can affect bullets far more than most would guess at 100 yards. (And no, "hunderd" is not a typo.)
As my article mentions, a barrel "walking" as it heats up can be due to other factors, including barrel bedding, and how well its fitted to the action. But no, properly heat-treated barrels (even very light ones) should not shoot to different places as they started heating up--certainly not within the first three shots. (One of the LEAST stable barrels I've ever fired was a really heavy "varmint" .22-250 barrel on a brand of factory rifle known for good accuracy. Within 3-4 shots it would start shooting higher and to the right.)
As I noted at the beginning of this thread, everything noted by the OP can be easily explained by normal variation--especially of 3-shot groups.
