Modern mammals, birds, and non-avian reptiles have shared developmental and evolutionary origins in the ancestral amniotes of 300 million years ago. A previous analysis of a newly completed dataset on the cellular composition of the major parts of the brain of 242 amniote species, generated using the same cell counting method, the isotropic fractionator, argued for changes in the body-brain relationship in amniote evolution (Kverkova et al., 2022), but did not explore how the brains of amniotes diverged in their neuronal composition. Here I show, using the same dataset but focusing instead on the cellular composition of the brains regardless of body mass and phylogenetic relatedness, that the brains of extant mammalian, avian, and non-avian reptile species are characterized by signature proportions of numbers of neurons across the pallium, the cerebellum, and the rest of brain. An increase to a higher, fixed proportion of 4.5 neurons in the cerebellum to every neuron in the rest of brain, with variable numbers of pallial neurons, characterizes the avian brain compared to other reptiles, whereas mammalian brains are characterized by an average 4 neurons in the cerebellum to every neuron in the pallium regardless of numbers of neurons in the rest of brain, which also differs from the proportion in most non-avian reptilian brains of 1.4 neurons in the pallium and 0.5 neuron in the cerebellum to every neuron in the rest of brain. Thus, the independent evolution of endothermy in birds and mammals occurred with dramatic increases in numbers of neurons in all brain structures that differed markedly between birds and mammals. Additionally, there are marked continuities in the scaling of extant amniote brains that allow for the neuronal composition of the brain of ancestral amniotes to be estimated. Using these similarities in the neuronal scaling rules between living mammals and non-avian reptiles, I provide scaling relationships that allow predicting the composition of early mammaliaform and synapsid brains in amniote evolution, and I propose a simple model of amniote brain evolution that accounts for the diversity of modern mammalian, avian, and non-avian reptilian brains with only a few clade-shifting events in brain connectivity between cerebral cortex and cerebellum in mammals and between the cerebellum and rest of brain in birds, building on the increased availability of energy supply to the brain associated with the evolution of the increased oxidative and cardiovascular capacities that underlie endothermy.