Temperature is one of the fundamental environmental variables that determine the composition and function of microbial communities. However, a predictive understanding of how microbial communities respond to changes in temperature is lacking, partly because it is not obvious which aspects of microbial physiology determine whether a species could benefit from a change in the temperature. Here we incorporate how microbial growth rates change with temperature into a modified Lotka-Volterra competition model and predict that higher temperatures should-in general-favour the slower-growing species in a bacterial community. We experimentally confirm this prediction in pairwise cocultures assembled from a diverse set of species and show that these changes to pairwise outcomes with temperature are also predictive of changing outcomes in three-species communities, suggesting that our theory may be applicable to more-complex assemblages. Our results demonstrate that it is possible to predict how bacterial communities will shift with temperature knowing only the growth rates of the community members. These results provide a testable hypothesis for future studies of more-complex natural communities and we hope that this work will help to bridge the gap between ecological theory and the complex dynamics observed in metagenomic surveys.