Some points:
(1) As Tom pointed out, T. rex is nested within an Asian subclade of giant (sauropod-killer?!) Tyrannosaurinae.
(2) The presence of T. rex in Laramidia immediately follows a eustatic draw-down, which exposed Beringia to the air. This implies that T. rex itself originated in Asia and then dispersed into Laramidia. This sets up the prediction that bona-fide T. rex will be found in the youngest Cretaceous rocks in Asia.
(3) The quick dispersal of T. rex into Laramidia from Asia implies that its distribution across Asia was widespread,Âand that, combined with its large size, buffered it from the selective effects of the polar regions there.
(4) The polar tyrannosaurid of Laramidia is a basal tyrannosaurine, which is phylogeneticallyÂremote from the Asian tyrannosaurines, so it does not represent the ancestralÂstock of T. rex.
Therefore, it isn't a stretch to hypothesize that once Beringia surfaced, all T. rex had to do was walk across the land bridge and devastate Laramidia. Had that not occurred, we'd have unique endemic Laramidian tyrannosaurids in the Late Maastrichtian (i.e., new species of Albertosaurus, Nanuqsaurus, etc.).