Body size is a synthetic functional trait determining many key ecosystem properties. Reduction in average body size has been suggested as one of the universal responses to global warming in aquatic ecosystems. Climate change, however, coincides with human-enhanced dispersal of alien species and can facilitate their establishment. We address effects of species introductions on the size structure of recipient communities using data on Red Sea bivalves entering the Mediterranean Sea through the Suez Canal. We show that the invasion leads to increase in median body size of the Mediterranean assemblage. Alien species are significantly larger than native Mediterranean bivalves, even though they represent a random subset of the Red Sea species with respect to body size. The observed patterns result primarily from the differences in the taxonomic composition and body-size distributions of the source and recipient species pools. In contrast to the expectations based on the general temperature–size relationships in marine ectotherms, continued warming of the Mediterranean Sea indirectly leads to an increase in the proportion of large-bodied species in bivalve assemblages by accelerating the entry and spread of tropical aliens. These results underscore complex interactions between changing climate and species invasions in driving functional shifts in marine ecosystems.