1. The role of energy in ecological processes has hitherto been considered primarily from the standpoint that energy supply is limited. That is, traditional resource-based ecological and evolutionary theories and the recent 'metabolic theory of ecology' (MTE) all assume that energetic constraints operate on the supply side of the energy balance equation. 2. For endothermic animals, we provide evidence suggesting that an upper boundary on total energy expenditure is imposed by the maximal capacity to dissipate body heat and therefore avoid the detrimental consequences of hyperthermia--the heat dissipation limit (HDL) theory. We contend that the HDL is a major constraint operating on the expenditure side of the energy balance equation, and that processes that generate heat compete and trade-off within a total boundary defined by heat dissipation capacity, rather than competing for limited energy supply. 3. The HDL theory predicts that daily energy expenditure should scale in relation to body mass (M(b)) with an exponent of about 0.63. This contrasts the prediction of the MTE of an exponent of 0.75. 4. We compiled empirical data on field metabolic rate (FMR) measured by the doubly-labelled water method, and found that they scale to M(b) with exponents of 0.647 in mammals and 0.658 in birds, not significantly different from the HDL prediction (P > 0.05) but lower than predicted by the MTE (P < 0.001). The same statistical result was obtained using phylogenetically independent contrasts analysis. Quantitative predictions of the model matched the empirical data for both mammals and birds. There was no indication of curvature in the relationship between Log(e) FMR and Log(e)M(b). 5. Together, these data provide strong support for the HDL theory and allow us to reject the MTE, at least when applied to endothermic animals. 6. The HDL theory provides a novel conceptual framework that demands a reframing of our views of the interplay between energy and the environment in endothermic animals, and provides many new interpretations of ecological and evolutionary phenomena.