The relationship between resting energy expenditure (REE) (kJ/d) and body mass (M) (kg) is a cornerstone in the study of energy physiology. By expressing REE as a function of body mass observed across mammals, Kleiber formulated the now classic equation: REE = 293M(0.75). The biological processes underlying Kleiber's law have been a topic of long-standing interest and speculation. In the present report we develop a new perspective of Kleiber's law by developing an organ-tissue level REE model consisting of five components: liver, brain, kidneys, heart and remaining tissues. The resting thermal output of each component is the product of the component's specific resting metabolic rate (K) and mass (T). With increasing body size, the K values for all five components had negative exponents and were directly proportional to M(-0.08--0.27), and all component T values were directly proportional to M(0.76-1.01). The resulting exponents of the product (K x T) were M(0.60-0.86) for the five components. Although the (K x T) values of individual components do not scale equally, their combined formula (286M(0.76)) is similar to that observed by Kleiber on the whole-body level. Modeling mammalian REE at the organ-tissue level provides new insights and pathways for future mechanistic explorations of REE-body composition relationships.