The “radiator” theory of brain evolution is proposed to account for “mosaic evolution” whereby brain size began to increase rapidly in the genus Homo well over a million years after bipedalism had been selected for in early hominids. Because hydrostatic pressures differ across columns of fluid depending on orientation (posture), vascular systems of early bipeds became reoriented so that cranial blood flowed preferentially to the vertebral plexus instead of the internal jugular vein in response to gravity. The Hadar early hominids and robust australopithecines partly achieved this reorientation with a dramatically enlarged occipital/marginal sinus system. On the other hand, hominids in the gracile australopithecine through Homo lineage delivered blood to the vertebral plexus via a widespread network of veins that became more elaborate through time. Mastoid and parietal emissary veins are representatives of this network, and increases in their frequencies during hominid evolution are indicative of its development. Brain size increased with increased frequencies of mastoid and parietal emissary veins in the lineage leading to and including Homo, but remained conservative in the robust australopithecine lineage that lacked the network of veins. The brain is an extremely heatsensitive organ and emissary veins in humans have been shown to cool the brain under conditions of hyperthermia. Thus, the network of veins in the lineage leading to Homo acted as a radiator that released a thermal constraint on brain size. The radiator theory is in keeping with the belief that basal gracile and basal robust australopithecines occupied distinct niches, with the former living in savanna mosaic habitats that were subject to hot temperatures and intense solar radiation during the day.