The accuracy of predictive models (also known as mechanistic or causal models) of animal responses to climate change depends on properly incorporating the principles of heat transfer and thermoregulation into those models. Regrettably, proper incorporation of these principles is not always evident. We have revisited the relevant principles of thermal physiology and analysed how they have been applied in predictive models of large mammals, which are particularly vulnerable, to climate change. We considered dry heat exchange, evaporative heat transfer, the thermoneutral zone and homeothermy, and we examined the roles of size and shape in the thermal physiology of large mammals. We report on the following misconceptions in influential predictive models: underestimation of the role of radiant heat transfer, misassignment of the role and misunderstanding of the sustainability of evaporative cooling, misinterpretation of the thermoneutral zone as a zone of thermal tolerance or as a zone of sustainable energetics, confusion of upper critical temperature and critical thermal maximum, overestimation of the metabolic energy cost of evaporative cooling, failure to appreciate that the current advantages of size and shape will become disadvantageous as climate change advances, misassumptions about skin temperature and, lastly, misconceptions about the relationship between body core temperature and its variability with body mass in large mammals. Not all misconceptions invalidate the models, but we believe that preventing inappropriate assumptions from propagating will improve model accuracy, especially as models progress beyond their current typically static format to include genetic and epigenetic adaptation that can result in phenotypic plasticity.