Debatable, but the common consensus is that T-Rex had little to no feather. At the very least, the feathers couldn't have covered all of the body because T-Rex skin imprints have been found without feathers, tho they're not of all the skin, so there still may have been some feathered parts.

The idea that T-Rex had feathers didn't come from nowhere tho : We have many evidence of feathered dinosaurs from many groups. The T-Rex is niched within the coelurosauria clade, which includes many dinosaurs that are mostly covered in feathers (and even modern birds). There's even a close relative of T-Rex, Yutyrannus, with evidence of wide feather covering.

The reason why T-Rex didn't have that much feathers is likely the same reason why elephants aren't hairy : Big animals have less problem keeping heat, and may even at some point have problem evacuating excess heat (and yes, many dinosaurs were warm blooded). So as T-Rex got bigger, feathers became more of a hindrance.