Abstract Thermal performance within predator–prey systems may have profound effects on species interactions under climate change. However, how the thermal response of predators and prey to climate change affects their interactions is still understudied. To examine the responses of a predator–prey system to climate change, we constructed a biologically detailed stage‐structured population dynamic model using aphids (prey) and ladybirds (predator) as a model system. We explore the system's dynamics across the entire feasible parameter space of annual mean temperature and seasonality. Within this space, we explore all qualitatively possible scenarios of thermal performance mismatches to gain insight into how these affect the interacting species' responses to climatic change. We find that, generally, warmer and less seasonal climates are the most favourable climate conditions for both species. Our results also indicate that predation always has a stronger effect on aphid abundance than the climate in tropical and subtropical regions for all the thermal performance mismatch scenarios. Furthermore, predation's (biotic) effect on prey abundance will generally decrease relative to the effect of climate (abiotic) when future climates become warmer and more seasonal. Our research highlights that the effects of increasing seasonality are consistent with climate having a proportionally larger impact on species pairs with different thermal performances than predation. Read the free Plain Language Summary for this article on the Journal blog.