As selection acts on multivariate phenotypes, the evolution of traits within populations not only depends on the genetic basis of each trait, but also on the genetic relationships among traits. As metabolic rate is often related to vital traits such as growth, physiology and behaviour, its variation and evolution is expected to have important repercussions on individual fitness. However, the majority of the correlations between metabolic rate and other traits has been based on phenotypic correlations, while genetic correlations, basis for indirect selection and evolution, have been overlooked. Using a case study, we explore the importance of properly estimating genetic correlations to understand and predict evolution of multivariate phenotypes. We show that selection on metabolic traits could result in indirect selection mainly on growth-related traits, owing to strong genetic correlations, but not on swimming or risk-taking and sociability behaviour even if they covary phenotypically. While phenotypic correlation can inform about genetic correlation direction, caution is needed in predicting the magnitude of genetic correlation. Therefore, even though phenotypic correlations among physiological and behavioural traits could be useful, deriving evolutionary conclusions based purely on them is not robust. In short, proper estimation of genetic correlations is needed when predicting evolutionary consequences. This article is part of the theme issue ‘The evolutionary significance of variation in metabolic rates’.