Concern about climate change has spurred experimental tests of how warming affects species' abundance and performance. As this body of research grows, interpretation and extrapolation to other species and systems have been limited by a lack of theory. To address the need for theory for how warming affects species interactions, we used consumer-prey models and the metabolic theory of ecology to develop quantitative predictions for how systematic differences between the temperature dependence of heterotrophic and autotrophic population growth lead to temperature-dependent herbivory. We found that herbivore and plant abundances change with temperature in proportion to the ratio of autotrophic to heterotrophic metabolic temperature dependences. This result is consistent across five different formulations of consumer-prey models and over varying resource supply rates. Two models predict that temperature-dependent herbivory causes primary producer abundance to be independent of temperature. This finding contradicts simpler extensions of metabolic theory to abundance that ignore trophic interactions, and is consistent with patterns in terrestrial ecosystems. When applied to experimental data, the model explained 77% and 66% of the variation in phytoplankton and zooplankton abundances, respectively. We suggest that metabolic theory provides a foundation for understanding the effects of temperature change on multitrophic ecological communities.