Responding to perceived threats is energetically expensive and can require animals to curtail somatic repair, immunity, and even reproduction to balance energy ledgers. In birds and mammals, energetic demands of thermoregulation are often immense, yet whether homeostatic body temperatures are also compromised to aid the stress response is not known. Using data sourced from over 60 years of literature and 24 endotherm species, we show that exposure to non-thermal challenges (e.g. human interaction, social threats) caused body temperatures to decrease in the cold and increase in the warmth, but particularly when species-specific costs of thermoregulation were high and surplus energy low. Biophysical models revealed that allowing body temperature to change in this way liberated up to 24% (mean = 5%) of resting energy expenditure for use towards coping. While useful to avoid energetic overload, these responses nevertheless heighten risks of cold- or heat-induced damage, particularly when coincident with cold- or heatwaves.