Transgenic growth hormone (TG) mice (Mus musculus L., 1758) obtain enhanced growth via compensatory feeding at intermediate sizes and via higher growth efficiency. The latter involves diverting resources from other functions such as locomotion and wakefulness. Thermogenesis is a major expense for small mammals, so we explored whether TG mice express a trade-off between growth and thermoregulation. TG mice are hypothermic and cannot maintain their body temperature under cold stress. TG mice showed initial enlargement of brown adipose tissue and subsequent age-related decreases not seen in controls. Some TG mice became torpid after fasting durations not known to affect other mice. On a high-calorie diet, TG mice had higher body temperatures even though controls did not. Our background strain developed obesity on a high-protein and high-fat diet, and on a diet supplemented with carbohydrates, whereas TG mice never developed obesity. White adipose tissue deposits of TG females were relatively larger, but those of TG males were relatively smaller, than those of controls fed standard food. We also found significant effects of the three experimental diets, as well as gender, age, body mass, ambient temperature, and behavioural activity, on rectal temperatures of TG mice and controls in a large breeding colony. Thermogenesis of TG mice fed standard food appears energetically constrained, likely contributing to enhanced growth efficiency.