Based on T.rex skin impressions alone we can conclude that adults were not entirely covered with feathers, and also factoring in the immense size of the animal, heat dispersal becomes an issue and feathers would have only served to insulate and trap heat in a multi-ton endotherm, making the existence of feathers far outside the realm of possibility in T.rex. This is also why elephants, hippos, and rhinos look the way they do, devoid of coats of fur.
T.rex young are commonly depicted with down fluff, and rightly so being that, while small, T.rex young had a much higher ratio of surface area to cumulative volume than adult organisms, and wouldn't have retained heat as well. Young Tyrannosaurs shedding down as they grow is easily applicable to both birds and reptiles today which molt their feathers and scales respectively as they mature.
Saw that Brusatte book myself, and depicting the tyrannosaurids with ornamental proto-feathers isn't entirely implausible. Losing down fluff and having proto-feathers emerge sporadically in some areas is possible, but the book has them around the head, and T.rex would have lost a lot of heat cranially; again, the insulation in that region, while it looks neat in the book, isn't likely.