It's funny how thinking of an anthropomorphic Tyrannosaur sporting a human hairstyle is much closer to the actual probably integument of Tyrannosaurus than all those TV shows and movies that set it out to be this cool, scaly-looking thing, though some at least have the dignity of admitting they were wrong (Walking with Dinosaurs at least acknowledged the birds are dinosaurs deal in-show, but kept the featherlessness of the coelurosaurs in all their subsequent programs for everyone sans birds up until the panned movie, and gorgosaurus is still noticably featherless). The recent discovery of that patch of tyrannosaur skin, previous evidence pointing to mosaic scales, and Yutyrannus makes me feel justified that Tyrannosaurus and its subtropical kin had both to varying degrees.
Moreover, non-pennaceous feathers kinda look like hair. One can't help but imagine a T. rex with a dodgy toupee or a beard to top everything off, but that's veering into speculative territory, and not in a good way.
We tend to see birds as wimpy, culturally speaking, and the whole "birds are the true heirs of the dinosaurs" and "some dinosaurs definitely had feathers," kinda hit us straight in the mammalian pride. Funnily enough, no one bothered to complain when we started portraying cynodonts with hair, even though the evidence for it is tenuous.