The warm blodded theory is the way I lean as well. Birds are dinosaurs closest living relatives, and birds are warm blooded. Also, as we know, fish are cold blooded, but the great white is warm blooded.
Being the devils advocate, all known preditors also scavenge if the opportunity presents itself, so T-Rex being a preditor still makes sense. It may not have been the most efficient HUNTER, scavenging more often then not, but I believe it was still capable of ambush hunting if nothing else.

I'd say both. Top predators tend to use their size or number to take the kill from other smaller preditors as well as general carrion; but I'd be surprised if T-Rex didn't hunt and kill its prey, either straight away or wounding it sufficiently (through blood loss/ bacterial infection/blood poisoning) and tracking the prey 'til it was weak enough to finish off. In terms of hunting technique, I read the suggestion that its hunting technique was probably similar to Great Whites in that they would ambush their prey (if we're certain T-Rexs lacked speed), and bite large chunks out of their prey (the forearms redundant) before finishing them off.

It's occurred to me too that the big predatory dinosaurs probably considered hadrosaurs their standard prey. Big enough to be worth the trouble, and with fairly puny natural weapons for their size. They probably ran from big flesh-eaters, but I'm not sure that they would have been much faster runners. Maybe they took refuge in the water (though the waters of the Cretacaeous had dangers all their own).

Modern mammalian carnivores also tend to look for a small, old, sickly, or injudred herd beast to attack. Most herd-dwelling herbivores (elephants and musk oxen are significant exceptions) will stampede away from an attacking carnivore, leaving the weakest in their herd to perish. Cruel, but it comes directly from the logic of their selfish genes -- they are more related to themselves than to anyone else in the herd, and each would put itself in very severe danger by fighting.

Dinosaurian herbivores probably behaved the same way. So even if a big biped like a tyrannosaur was a relatively slow runner, it might be that the specific herbivore he was chasing might be an even _slower_ one. The ceratopsians had a choice to run or fight; the decision probably depended on the size of the attacker, the size of the herd, and the type of ceratopsians (some of the ceratopsians were no great shakes as fighters). Looking at the anklyosaurs it's really difficult to envision them "running" at anything but a fast waddle; all that armor and nasty tail-knobbery and spikery was clearly meant to let the beast stand its ground. Sauropods might have done a number of things depending on relative size; the reaction of a really big sauropod to a small carnivorous dinosaur was probably to tail-whip or trample, rather than flee. I don't know how fast big sauropods ran (or, technically, "walked"); they would have been clumsy with all their inertia, but sometimes a big animal can be surprisingly fast based on stride length (example: elephants, who can walk fast enough to keep up with a running horse and easily run down a running man).

But yes, I really really doubt that a big hungry carnivorous dinosaur would have passed up an opportunity to scavenge, whether by being first on the scene or by hijacking it from some other animals.

- Jordan