Perhaps the greatest mystery surrounding dinosaurs concerns whether they were endotherms, ectotherms, or some unique intermediate form. Here we present a model that yields estimates of dinosaur body temperature based on ontogenetic growth trajectories obtained from fossil bones. The model predicts that dinosaur body temperatures increased with body mass from approximately 25 degrees C at 12 kg to approximately 41 degrees C at 13,000 kg. The model also successfully predicts observed increases in body temperature with body mass for extant crocodiles. These results provide direct evidence that dinosaurs were reptiles that exhibited inertial homeothermy.