Despite numerous studies, the thermal physiology of dinosaurs remains unresolved. Thus, perhaps the commonly asked question whether dinosaurs were ectotherms or endotherms is inappropriate, and it is more constructive to ask which dinosaurs were likely to have been endothermic and which ones ectothermic. Field data from crocodiles over a large size range show that body temperature fluctuations decrease with increasing body mass, and that average daily body temperatures increase with increasing mass. A biophysical model, the biological relevance of which was tested against field data, was used to predict body temperatures of dinosaurs. However, rather than predicting thermal relations of a hypothetical dinosaur, the model considered correct paleogeographical distribution and climate to predict the thermal relations of a large number of dinosaurs known from the fossil record (>700). Many dinosaurs could have had “high” (≥30°C) and stable (daily amplitude ≤2°C) body temperatures without metabolic heat production even in winter, so it is unlikely that selection pressure would have favored the evolution of elevated resting metabolic rates in those species. Recent evidence of ontogenetic growth rates indicates that even the juveniles of large species (3000–4000 kg) could have had biologically functional body temperature ranges during early development. Smaller dinosaurs (<100 kg) at mid to high latitudes (>45°) could not have had high and stable body temperatures without metabolic heat production. However, elevated metabolic rates were unlikely to have provided selective advantage in the absence of some form of insulation, so probably insulation was present before endothermy evolved, or else it coevolved with elevated metabolic rates. Superimposing these findings onto a phylogeny of the Dinosauria suggests that endothermy most likely evolved among the Coelurosauria and, to a lesser extent, among the Hypsilophodontidae, but not among the Stegosauridae, Nodosauridae, Ankylosauridae, Hadrosauridae, Ceratopsidae, Prosauropoda, and Sauropoda.