Predictions of species responses to climate change often focus on distribution shifts, although responses can also include shifts in body sizes and population demographics. Here, shifts in the distributional ranges (‘climate space’), body sizes (as maximum theoretical body sizes, L∞) and growth rates (as rate at which L∞ is reached, K) were predicted for five fishes of the Cyprinidae family in a temperate region over eight climate change projections. Great Britain was the model area, and the model species were Rutilus rutilus, Leuciscus leuciscus, Squalius cephalus, Gobio gobio and Abramis brama. Ensemble models predicted that the species' climate spaces would shift in all modelled projections, with the most drastic changes occurring under high emissions; all range centroids shifted in a north-westerly direction. Predicted climate space expanded for R. rutilus and A. brama, contracted for S. cephalus, and for L. leuciscus and G. gobio, expanded under low-emission scenarios but contracted under high emissions, suggesting the presence of some climate-distribution thresholds. For R. rutilus, A. brama, S. cephalus and G. gobio, shifts in their climate space were coupled with predicted shifts to significantly smaller maximum body sizes and/or faster growth rates, aligning strongly to aspects of temperature-body size theory. These predicted shifts in L∞ and K had considerable consequences for size-at-age per species, suggesting substantial alterations in population age structures and abundances. Thus, when predicting climate change outcomes for species, outputs that couple shifts in climate space with altered body sizes and growth rates provide considerable insights into the population and community consequences, especially for species that cannot easily track their thermal niches.