Two frequently debated aspects of hominin evolution are the development of upright bipedal stance and reduction in body hair. It has long been argued, on the basis of heat-balance models, that thermoregulation might have been important in the evolution of both of these traits. Previous models were based on a stationary individual standing in direct sunlight; here we extend this approach to consider a walking hominin, having argued that walking is more thermally challenging than remaining still. Further, stationary activities may be more compatible with shade seeking than activities (such as foraging) involving travel across the landscape. Our model predictions suggest that upright stance probably evolved for nonthermoregulatory reasons. However, the thermoregulatory explanation for hair loss was supported. Specifically, we postulate progressive hair loss being selected and this allowing individuals to be active in hot, open environments initially around dusk and dawn without overheating. Then, as our ancestors' hair loss increased and sweating ability improved over evolutionary time, the fraction of the day when they could remain active in such environments extended. Our model suggests that only when hair loss and sweating ability reach near-modern human levels could hominins have been active in the heat of the day in hot, open environments.