Nowadays thanks to modern scientific techniques and new fossile finds we know that's not true. For one thing, T. rex's bones were found to be hollow, with the exception of the legs. Allosaurus' bones were solid throughout its body. For another, smaller members of the tyrannosaur family such as Daspletosaurus and Albertosaurus bear a striking resemblence to the raptors like Deinonychus.
Recently in Mongolia, the earliest ever known member of the tyrannosaur family was a found, a little guy that scientists named Dilong paradoxus, or Paradoxical Dragon Emperor. What made him so amazing was: he had FEATHERS!!! That's right folks, T. rex's great, great, great grandpa was a little feathered fellow (as I like to call those cute feathered dinosaurs they've been finding in Yixian, China recently). Having feathers means that Dragon Emperor was warmblooded and needed the feathers for insulation due to his small size. Dilong migrated west from China into Europe and North America, growing bigger as it went. It grew into Daspletosaurus, then Albertosaurus and finally T. rex.
T. rex adults didn't have feathers because they were too big to need them. The young however, would have. They were warmblooded, but would've frozen to death if they'd hatched with no covering, due to their being so tiny. So it's likely hatchling T. rexes had down till they grew to their juvenile stage and then would've shed them around that time.
Other ways T. rex was like a bird: Recently it was found that T. rex's breathing system was very similar to modern birds. Originally it was thought to be like a crocs, but this wasn't the case. How they can tell just from a skeleton is beyond me, but I guess they know what they're doing.
The most exciting thing though was the discovery of medullary (egg-laying) bone on the leg bone of T. rex skeleton that was recently found. For the first time scientists can tell the gender of the animal. The medullary bone is only found in female birds that are ready to lay eggs. Reptiles don't get this! So now they have found two distinctly avioid traits among tyrannosaurs: feathers and medullary bone. This is a very exciting time to be a dinosaur fan!
So when I think of T. rex, I'll end up thinking of Big Bird instead of Godzilla. XP
Articles on this: Feathered Ancestor of T. rex Unearthed
Dinosaur Fossil Bone leads to gender, age determinations
Birds of a Feather