A component of metabolic scaling theory has worked towards understanding the influence of metabolism over the generation and maintenance of biodiversity. Specific models within this 'metabolic theory of biodiversity' (MTB) have addressed temperature gradients in speciation rate and species richness, but the scope of MTB has been questioned because of empirical departures from model predictions. In this study, we first show that a generalized MTB is not inconsistent with empirical patterns and subsequently implement an eco-evolutionary MTB which has thus far only been discussed qualitatively. More specifically, we combine a functional trait (body mass) approach and an environmental gradient (temperature) with a dynamic eco-evolutionary model that builds on the current MTB. Our approach uniquely accounts for feedbacks between ecological interactions (size-dependent competition and predation) and evolutionary rates (speciation and extinction). We investigate a simple example in which temperature influences mutation rate, and show that this single effect leads to dynamic temperature gradients in macroevolutionary rates and community structure. Early in community evolution, temperature strongly influences speciation and both speciation and extinction strongly influence species richness. Through time, niche structure evolves, speciation and extinction rates fall, and species richness becomes increasingly independent of temperature. However, significant temperature-richness gradients may persist within emergent functional (trophic) groups, especially when niche breadths are wide. Thus, there is a strong signal of both history and ecological interactions on patterns of species richness across temperature gradients. More generally, the successful implementation of an eco-evolutionary MTB opens the perspective that a process-based MTB can continue to emerge through further development of metabolic models that are explicit in terms of functional traits and environmental gradients.