Although climate-based hypotheses are widely used to explain large-scale diversity patterns, they fall short of explaining the spatial variation among taxonomic groups. Integrating food web and metabolic theories into macroecology is a promising step forward, as they allow including explicit taxon-specific traits that can potentially mediate the relationship between climate and diversity. Our investigation focuses on the role of body size and trophic structure in mediating the influence of contemporary climate and historical climate change on global tetrapods species richness. We used piecewise structural equation modeling to assess the direct effects of contemporary climate and climate instability of species richness and the indirect effects of climate on tetrapod richness mediated by community-wide species traits. We found that birds and mammals are less sensitive to the direct effect of contemporary climate than amphibians and squamates. Contemporary climate and climate instability favored the species richness of mammals and amphibians. However, for birds and squamates, this link is only associated with contemporary climate. Moreover, we showed that community-wide traits are correlated with species richness gradients. However, we highlight that this relationship is dependent upon the specific traits and taxonomic groups. Specifically, bird communities with smaller bodies and bottom-heavy structures support higher species richness. Squamates also tend to be more diverse in communities with prevalence of smaller bodies, while mammals are correlated with top-heavy structures. Moreover, we showed that higher contemporary climate and climate instability reduce the species richness of birds and mammals through community-wide traits and indirectly increase squamate species richness. We also showed that body size and trophic structure are driving a global asymmetric response of tetrapod diversity to climate effects, which highlights the limitation to use the "typical" climate-based hypotheses. Furthermore, by combining multiple theories, our research contributes to a more realistic and mechanistic understanding of diversity patterns across taxonomic groups.