There's been a study that's been making headlines recently, in which it's concluded that pretty much every non-avian dinosaur (including Archaeopteryx) is a mesotherm.
"Mesothermic" is a very fuzzy definition which essentially means intermediate between cold-blooded (ectothermic) animals like reptiles, amphibians and most fish, and warm-blooded (endothermic) animals like mammals and birds. The broad definition of a "dinosaur" nowadays is an intermediary form between birds and archosaurian reptiles, so this probably won't surprise you.
The most notable modern mesotherms are lamnid sharks (incl. great white and mako), swordfish, tuna and monotreme mammals (echidna and platypus). They have several methods of generating and retaining heat, but have fewer systems of temperature control than an endotherm, and are therefore less energy efficient and more dependant on environmental conditions.
The study was performed by measuring growth rates in 21 dinosaur species, and comparing them with a large number of present-day animals.
So, that's the news. Personally though I don't agree, and think the study has serious problems.
The reason is, growth rates are not on a fixed scale dictated solely by metabolism. It's made possible by burning off energy, but various factors can determine how much excess energy an animal has to put into growth. It's determined by how much nutrition the animal is receiving, and how much energy it's burning off due to its lifestyle.
Today's warm-blooded animals tend to have lifestyles in which the babies are highly dependant on their parents - they don't travel much, and rely on the adults to protect them and feed them. The adults are able to provide them with far more nutrition than a small animal could ever find on its own; either through calorie-rich milk in mammals, or the all-day foraging cycle of birds (and there's almost always two adults caring for a chick).
Basically, a young mammal/bird has little more requirement than to sit around, get used to how its body works, eat and grow. They can put a HUGE amount of energy into their growth, because they've got so much to spare. They're close to (or at) full growth by the time they leave their parents.
But dinosaurs were different. Most or all of them had to fend for themselves well before adulthood, and most seem to have been from a very early age. Some of them may have been independant from the moment they hatched.
This means they wouldn't get nearly as much nutrition as today's warm-blooded animals, without milk or a full-sized food provider. But there's more to it than that: an independant animal has to burn off energy on travel, evading predators, finding their food, and even digesting it (mammal and bird parents do most of the digestion for their offspring).
Therefore it's inevitable that a dinosaur would grow more slowly than one of today's warm-blooded animals, due to lifestyle. It's not a smoking gun about their metabolism.
It's worth noting that growth rates do vary among dinosaurs. Ceratopsids, ornithopods, tyrannosaurids and large sauropods all grow quicker than their relatives. And interestingly, most of those (sauropods being the exception I think, which baffles me) also seem to have raised their babies for extended periods.
Anyway. As for what sort of metabolism dinosaurs had, the one certainty is that it seemed to be highly variable.
Some very early dinosaurs show definite signs of advanced ectothermy, as prosauropods demonstrate a mish-mash of growth rates (within species and even within groups), which probably show animals that were getting more sun and environmental warmth growing faster.
Some dinosaur groups had better heat insulation than others, a sure sign that they were less dependant on sunbathing to warm their bodies.
And the respiratory system in each dinosaur order grew increasingly sophisticated and capable over time. I think this is a sign of the progression of dinosaur energetics.
It's perfectly plausible that maniraptoran dinosaurs may have had metabolisms on par with today's ground birds, and ornithopods may have had energetics similar to mammals. But it's an issue that's been debated almost as long as palaeontology's been in existence.
(There's more
here. I recommend following Phenomena, it's where I get most of my dinosaur news. You may find a similar post to this in the comments section; it ain't plagiarism.)
Sigh, once again my lengthy typing has exposed me for a brutal ninja'ing. Cheers, Shrimp.