Understanding how global warming shapes species evolution within communities is a pressing goal of ecology. Temperature affects interacting species and can lead to changes in species interactions, but how that will alter species evolutionary trajectories within complex food webs is poorly understood. Here we address 1) whether different predators affect prey evolution differentially, 2) whether the food web context in which this happens influences prey evolution, 3) whether temperature affects prey evolution directly, and 4) whether ecological interactions mediate how temperature affects prey evolution. We use a combination of mathematical modeling and experimental evolution assays in microbial food webs composed of prey algae and their protists predators. We found that temperature alone doesn't drive prey evolution unless predators are involved. Importantly, the influence of temperature through predation is contingent on the food web structure. This leads to distinct evolutionary trajectories when prey evolves with predators alone or with a competing predator present. Our findings indicate that the species evolution to warming is likely contingent on their specific ecological contexts, suggesting that similar species across different food webs could exhibit diverse evolutionary responses to new climates.