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In the context of diversity gradients, the metabolic theory of ecology (MTE) posits that the logarithm of species richness should decrease linearly with the inverse of temperature, resulting in a specific slope. However, the empirical validity of this model depends on whether the data do not violate certain assumptions. Here, we test the predictions of MTE evaluating all of its assumptions simultaneously. We used Neotropical freshwater fish and tested whether the logarithm of species richness varied negatively and linearly with temperature, resulting in the slope value specified by the MTE. As we observed that the assumption of the energetic equivalence of populations was not achieved, we also analyzed whether the energetic nonequivalence of populations could be responsible for the possible lack of fit to the MTE predictions. Our results showed that the relationship between richness and the inverse of temperature was linear, negative and significant and included the slope value predicted by the MTE. With respect to the assumptions, we observed that there was no spatial variation in the average energy flux of populations or in the body size and abundance of species. However, the energetic equivalence of populations was not achieved and the violation of this assumption did not affect the predictive power of the model. We conclude that the validity of the assumptions (spatial invariance in the average flux energy of populations and spatial invariance in the body size and abundance, especially) is required for the correct interpretation of richness patterns. Furthermore, we conclude that MTE is robust in its explanation of diversity gradients for freshwater fish, proving to be a valuable tool in describing ecological complexity from individuals to ecosystems. [ABSTRACT FROM AUTHOR]