Ocean warming and acidification alter the physiological performance and behaviour of many small‐bodied fishes, yet the potential interactive effects of these stressors on larger predators remains poorly understood. In particular, the combined effects of elevated temperature on metabolism and of elevated CO2 on the behaviour of large predators may not only affect their foraging behaviour, but also the communities in which their prey live. We used a factorial design to assess how projected warming and acidification create synergies or antagonisms between physiological and behavioural processes, such as swimming activity and feeding behaviour through odour tracking and vision. Temperature increased swimming activity during feeding, independent of CO2. Although temperature also increased motivational drive to locate and accept prey, elevated CO2 negated chemical and visual behavioural responses that enable effective hunting. Fundamental to these effects was the negligible effect of high CO2 in isolation, but its power to negate the positive effects of temperature when brought in conjunction. The reduced potential to locate prey due to the interactive effects of ocean acidification and warming, in combination with increases in energetic demand, suggests that energetic tradeoffs will be needed for sharks to sustain themselves at an individual and population level in a future ocean.