[QUOTE=John Mace]
What their original purpose was, we may never no. They may have been part of courtship displays, for conserving body heat, or any number of things. But they clearly weren’t for flight. It is thought that young T-Rexes had feathers, but lost them as they got older. Maybe that help them conserve body heat in a way that a larger animal might not need.
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In my opinion, the most likely reason they first evolved was for insulation. Theropods most likely were homeotherms (“warm-blooded”). The smaller forms would have required some way to prevent heat loss even in tropical climates.
AFAIK there is no direct evidence for feathers in T. rex. However, since the tyrannosaurs were quite closely related to the small theropods that did have feathers, it is interesting to think that they may have had them. As you say, they may have only been necessary in younger individuals. Adults would have had a smaller ratio of surface area to mass, and thus retained heat better and not needed them.
There is no reason to imagine that they were used for heat dissipation. The outer parts of feathers have no blood supply and being made of a material that conducts heat poorly would have no capacity to dissipate body heat.
In fact, the feathered dinosaurs that have been found, including Velociraptor, long postdate Archeopteryx in the fossil record. This has lead some to postulate that these feathered non-flying forms are actually descended from ancestors that could fly, like Archeopteryx. (Interestingly, Archeopteryx seems to possess a raptorial claw like that of the dromeosaurs like Velociraptor.) I find this a quite interesting scenario, though far from demonstrated.
Whatever the case, it is very clear at this point that the line between flying feathered avian dinosaurs like Archeopteryx, non-flying avian dinosaurs like Mononykus and Shuvuuia, feathered non-avian non-flying dinosaurs like Beipiaosaurus, Caudipteryx, Dilong, Protarchaeopteryx, Sinornithosaurus, Sinosauropteryx, and Jinfengopteryx, and flying feathered non-avian dinosaurs like Microraptor is very obscure. It is highly disputed where exactly to draw the line between “avian” and “non-avian” lineages; which of these feathered and flying forms belonged to which lineage; and whether non-flying feathered forms might have descended from flying forms.