Warming can impact consumer-resource interactions through multiple mechanisms. For example, warming can both alter the rate at which predators consume prey and the rate prey develop through vulnerable life stages. Thus, the overall effect of warming on consumer-resource interactions will depend upon the strength and asymmetry of warming effects on predator and prey performance. Here, we quantified the temperature dependence of both 1) density-dependent predation rates for two dragonfly nymph predators on a shared mosquito larval prey, via the functional response, and 2) the development rate of mosquito larval prey to a predator-invulnerable adult stage. We united the results of these two empirical studies using a temperature- and density-dependent stage-structured predation model. Warming accelerated both larval mosquito development and increased dragonfly consumption. Model simulations suggest that differences in the magnitude and rate of predator and prey responses to warming determined the change in magnitude of the overall effect of predation on prey survival to adulthood. Specifically, we found that depending on which predator species prey were exposed to in the model, the net effect of warming was either an overall reduction or no change in predation strength across a temperature gradient. Our results highlight a need for better mechanistic understanding of the differential effects of temperature on consumer-resource pairs to accurately predict how warming affects food web dynamics.