It is widely held that selective brain cooling, the lowering of brain temperature below arterial blood temperature, and adaptive heterothermy, the use of heat storage to reduce body water loss by evaporation, are crucial for the survival of large mammals in arid-zone habitats. These ideas arose 35 years ago as a consequence of work popularised on the eland and the oryx. However, brain temperature in these antelope was never measured. Also, the evidence that these large antelope use adaptive heterothermy was derived from experiments using captive animals. The development of miniature devices for remote sensing of body temperature now has allowed temperatures of free-living animals in their natural habitats to be recorded. With the exception of dehydrated Arabian oryx exposed to severe heat, free-living eland and oryx do not exhibit adaptive heterothermy, and have a mean body temperature at night higher than that during the day. Eland and oryx exhibit selective brain cooling of small magnitude (<0.5 °C) sporadically, at rest under moderate heat load. The view that eland and oryx routinely use adaptive heterothermy to save water and selective brain cooling to protect the brain is misleading, and arises from inadequate measurement or from depriving animals of access to thermoregulatory behaviour.