Global warming compels larger endothermic animals to adapt either physiologically or behaviourally to avoid thermal stress, especially in tropical ecosystems. Their adaptive responses may however be compromised by other constraints, such as predation risk or starvation. Using an exceptional camera-trap dataset spanning 32 protected areas across southern Africa, we find that intermediate-sized herbivores (100-550 kg) switch activity to hotter times of the day when exposed to predation by lions. These herbivores face a tight window for foraging activity being exposed to nocturnal predation and to heat during the day, suggesting a trade-off between predation risk and thermoregulation mediated by body size. These findings stress the importance of incorporating trophic interactions into climate change predictions.