Heat waves – extended periods of abnormally hot weather – are predicted to increase in severity and frequency under climate change. The severity of heat waves should impact communities and food webs through effects on performance of individual species and through changes in the strength of interactions between them. This study tested the effects of severity of simulated heat waves, with daily maxima of either 32°C or 40°C, on a tritrophic food web consisting of plants, Capsicum anuum, aphids, Myzus persicae and two parasitoids, Aphidius matricariae and Aphelinus abdominalis. Osmolarity of plant sap (concentration of dissolved solids) was highest under 40°C heat waves, suggesting the presence of secondary plant compounds involved with stress responses. Population growth of aphids was lower under heat waves (both 32°C and 40°C daily maxima), compared to environments with periodic hot days. Development time of parasitoids was longer under heat waves. Heat waves decreased the proportion of winged aphids in the population. When both parasitoid species were present, impacts on aphid populations were greater in heat wave environments than environments with periodic hot days. When either parasitoid species was by itself, heat waves did not affect the interaction between parasitoids and aphids. Numbers of A. matricariae were reduced in heat wave environments, whereas numbers of A. abdominalis were not. In addition to direct effects on individual species, we also obtained indirect evidence for the effects of heat waves on the bottom–up effects of plant stress compounds on herbivore performance, and on the strength of inter and intra-specific competition. Our results demonstrate that heat waves could have important effects on community structure, and on important, community-level processes such as intra-guild interactions and trophic cascades.