Abstract Climate warming may alter predator–prey interactions and predator feeding behaviour due to increased metabolic demands. How predators meet these increased demands may depend on trade‐offs in prey energy content and body size, handling time and other functional constraints. We tested hypotheses associated with these trade‐offs with the predatory mite Stratiolaelaps scimitus, and three prey that differed in body size, energy content, and defenses (Folsomia candida, Oppia nitens, and Carpoglyphus lactis). We estimated metabolic rate, predation in choice and no choice feeding trials, movement rate, and lipid and protein content for all four species at 16°C and 24°C. We used these data to estimate the predator's energy demands and compared these to estimated energy intake in the choice feeding trials. Predators had greater metabolic demands at 24°C than at 16°C, but temperature did not affect predator or prey movement rates. Warming decreased lipid content, but not protein content, of all three prey species, leading to lower energy content for C. lactis and O. nitens, but not F. candida. In both feeding trials at 24°C, predators increased their feeding on the smaller, energy‐poor C. lactis, but not the larger, energy‐rich F. candida, resulting in lower estimated energy intake. S. scimitus did not feed on O. nitens at either temperature. Predators increasingly fed on small‐bodied prey under warming and not the large‐bodied prey despite the potential for greater energetic gains from larger prey. We posit that predators minimized energy lost during feeding through lower handling costs associated with C. lactis, rather than maximize energy gain. We conclude that selection of prey based on body size changes with temperature as a trade‐off for predators to balance increased metabolic demands. As predators provide top‐down control and regulate energy flow through the consumption of their prey, changes to predator feeding behaviour with climate warming may affect food web dynamics and ecosystem‐level processes. Read the free Plain Language Summary for this article on the Journal blog.