Thomas E. Williamson of the New Mexico Museum of Natural History and Science is studying dinosaur fossils to answer this question. Here is his response:
"As yet, there is probably no evidence that would definitively prove whether or not some dinosaurs were warm-blooded. Scientists have explored numerous lines of evidence to try to answer this question.
"There is a clear difference in bone structure between modern cold-blooded and warm-blooded animals. Warm-blooded animals tend to have highly vascularized bone tissue. Cold-blooded animals, on the other hand, have relatively dense bone, sometimes even showing annual growth rings. Dinosaurs tend to have highly vascularized bone early in life and then develop dense bone with growth rings as they reach maturity. New evidence suggests that the different bone types are more related to growth rates than to warm- or cold-bloodedness.
"In modern animal communities, there are far fewer warm-blooded predators relative to prey than cold-blooded predators. This is because warm-blooded animals tend to eat far more than cold-blooded animals and so a given amount of prey will support far fewer warm-blooded predators. Unfortunately, it is very difficult to determine the actual relative abundance of predator versus prey from the fossils because the fossil record does not always preserve an accurate representation of the original animal community.
"Dinosaurs were able to survive even at high latitudes. For example, dinosaur fossils have been found in Alaska and Canada well above the Arctic Circle. During the time that these animals lived, however, the climate was generally much warmer than today's. It is also possible that these animals migrated into these areas during the warm summer months and retreated to lower latitudes ahead of the cold and long polar nights.
"Modern warm-blooded animals tend to have more erect postures than cold-blooded animals. Most dinosaurs have erect postures and therefore it has been suggested that this indicates that they had high activity levels and were warm-blooded. Along these lines, scientists have looked indirectly at the potential blood pressures of dinosaurs; warm-blooded animals tend to have relatively high blood pressures. Blood pressure can be estimated by looking at the vertical distance between the head and the heart. For some sauropod dinosaurs, this estimated blood pressure is very high indeed. Brachiosaurus would have a blood pressure of about 500 millimeters of mercury. This figure is about five times higher than that of a human. On the other hand, other dinosaurs--such as ceratopsians--would have a very low blood pressure, closer to that of living reptiles, based on this analysis.
"Modern warm-blooded animals have relatively larger brains than living cold-blooded animals. It is thought that large brains are needed to coordinate active, highly energetic animals. Most dinosaurs have very small brains relative to their body size. In fact, their brains closely resemble those of modern reptiles. A few small, predatory dinosaurs have relative brain sizes that are comparable with those of some living birds, such as ostriches, however.
"There is evidence from dinosaur trackways, mass accumulations of certain dinosaur fossils, and nesting sites that dinosaurs were social animals. Some have argued that such sophisticated behavior is suggestive of warm-bloodedness.
"Birds are warm-blooded and probably evolved from a group of meat-eating dinosaurs. Therefore, it has been argued, their dinosaur ancestors were also warm-blooded. But recent study of the bone structure of some of the earliest birds has revealed that it resembles that of modern cold-blooded reptiles, suggesting that the first birds were cold-blooded and that warm-bloodedness developed later.
"More recently, some researchers have looked for respiratory turbinates in the nasal passages of dinosaurs. Respiratory turbinates are fine, scroll-shaped bones found in the noses of most modern warm-blooded animals (mammals and birds). These structures are believed to function as moisture-recovery organs, recapturing water from warm and moist exhaled air. Without these structures, many warm-blooded animals would quickly dehydrate, especially in dry climates. So far, no respiratory turbinate structures have been found in dinosaurs. It has been argued, however, that many dinosaurs lived in warm and moist environments where water conservation may not have been important.