*puts nerd pants on*
You really want to talk about general integument, rather than feathers _per se_
But yes, first of all, we count birds as dinosaurs, and as such, 9000 current species of Maniraptoran dinosaurs have feathers, they can also fly (nerdness!!!)
I know I'm being pragmatic now, but bear with me
Stem-maniraptorans are the type of dinos you know from Jurassic Park etc, the Velociraptor as well as similar dinos, Oviraptor, Therizinosaurus. These *all* had feathers, as in - actual bird-feathers, including tail feathers, wing-feathers and some of them also had "leg-wings" (small Microraptorians were "4-winged" gliders)
Maniraptorans are coelurosaurian theropods, and we DO know that fur-like growth occur in stem-coelurosaurians (which include Tyrannosaur ancestors, but EXclude "carnosaurs" such as Allosaurus, or spectacular megalosaurids, such as Spinosaurus)
So, this means: Bird-feathers on Maniraptorans, and "fur" (or "proto-feathers") on primitive coelurosaurians, including Tyrannosaurids (Tyrannosaurus itself might have been secondarily scaled, like bird-feet are scaled, despite feathers on the rest of the body, but we know for a fact that early Tyrannosaurids, such as Yutyrannus were - not only fuzzy - but had a thick, fluffy covering, several centimetres thick, to protect from quite harsh winters)
NOW, this covers, as you suggested, the Theropods. Tracking fur/feathers any further back yields nothing. Abelisaurids are fairly primitive* theropods, and they are known from very definite scaly skin impressions, even similar to crocodiles
*primitive simply denotes something is further to the base of any selected evolutionary tree
THAT SAID
Early Ornithischians (Triceratops, Stegosaurus, Iguanodon - aka: all plant-eaters except the long-necked Sauropods) are known to have sported *thick, fluffy fur*
This is confusing to researchers. Sauropods show absolutely no sign of fur or feathers, and LATE Ornithischians, like Triceratops, Stegosaurus, Iguanodon, also show absolute scaly skin impressions in fossils.
Conclusion: In mid-to-late theropod lineage - and early-to-mid ornithischian lineage, fur appears. It MIGHT mean that the two examples share ancestry, meaning that fur occurs in common dinosaurian origin* (small "Ornithodirans" like Marasuchus and Lagerpeton) OR - they are examples of necesary and quite logical convergence, where - for environmental reasons - unrelated groups of animals end up growing similar kind of body covering.
*new research suggests a possibility of theropods+ornithischians sharing common ancestor separate from sauropods. This contradicts traditional model of theropods+sauropods, with ornithischians being separare. If the new model is correct, it explains some of the fur-issues.
(Some hardline proponents of this new model go as far as to exclude Sauropoda from the Dinosauria definition, but this has (thankfully) not been met with any acceptance)
The latter option (convergent evolution) is not too unheard of, after all - mammals grew their own version of fur, independent of dinosaur, and we sport it proudly - across our diversity, some more, some less, and humans are very good examples of how unpredictable these kinds of growths can be.
Think about it - lumps of fur here and there on our bodies, we are ugly as hell!
