Hurlburt, G. (2006) Relative brain size of small theropod dinosaurs indicates probable obligate endothermy. JVP 26(3) Abstracts pp.79

The large relative brain sizes of small theropod Cretaceous dinosaurs (Troodon, Ornithomimus, and Bambiraptor) probably required them to be visceral endotherms,
defined as endotherms whose high resting metabolic rate (BMR) depends on visceral organ metabolism. Their relative brain sizes were well within the relative brain size range of Recent endothermic amniotes (birds) and well above the range of Recent (nonavian) reptiles.

This proposal rests on the hypothesis that the relatively large brains of Recent visceral endotherms require both a high and controlled BMR. In all known ecto- and endothermic vertebrates,the central nervous system(CNS) uses 2-8% of basal metabolism, excepting 20% in Homo, and 11-13% in other primates. Although some elasmobranchs have large brains, the low metabolic rate of elasmobranch brains makes them metabolic equivalents of bony fish brains one-third their size, meaning their large relative brain size does not invalidate this hypothesis.

Dinosaur brain mass was estimated from endocasts, using brain-endocast ratios of adult alligators.Dinosaur relative brain sizes were calculated as EQs, which were based on brain-body equations of reptiles (REQ) and birds (BEQs). Ranges of reptile log (log10) REQs and bird log BEQs, were used because, unlike the corresponding EQs, they were normally distributed, validating use of Standard Deviations (SDs). Other than small theropods, dinosaur log REQs (-0.60 to 0.380; -3.0 to 2.0 SDs of the mean) were within both the actual range and two SDs of the mean of reptile log REQs (-0.41 to 0.39; -2.0t o +1.9 SDs of the mean). Small theropod log BEQs of -0.17 to -0.09 (1.05 to 0.58 SDs below the mean) were well within the range of bird log BEQs (-0.40 to 0.50; -2.33 to + 2 SDs of the mean); and within 1 SD of the bird log BEQ mean. The only ectothermic vertebrate even 3 SDs above the reptile log REQ mean is the elephant-nosed fish, (Gnathonemus, log REQ 0.64), at 3.3 SDs above the reptile mean. It devotes 60% of total body metabolism to the brain, an amount unknown and unlikely in terrestrial amniotes. Log REQs (-0.45 to 0.48) of other bony fish are -2.2 to +2.5 SDs of the reptile REQ mean.