Marine heatwaves are increasing in frequency and intensity, with potentially catastrophic consequences for marine taxa and ecosystems such as coral reefs. Environmentally realistic, extended heatwave and recovery time-series in a multi-stressor experimental framework can therefore provide enhanced predictive capacity for the performance of such systems under climate change. We exposed two common reef-building corals in Hawaiʻi, Montipora capitata and Pocillopora acuta, to a two-month period of high temperature and high pCO2 conditions (29.5C, ~1100 ppm) or ambient conditions (27.5C, ~500 ppm) in a factorial design, followed by two months of return to ambient conditions. In response to high temperature, but not high pCO2, multivariate physiology shifted through time in both species, driven by decreases in respiration rates and endosymbiont density. P. acuta exhibited more significantly altered physiology, and substantially higher bleaching and mortality than M. capitata. The species specific sensitivity of P. acuta appears to be driven by higher baseline rates of photosynthesis and lower initial host antioxidant capacity and thus sensitivity to reactive oxygen species under thermal stress. Thermal tolerance of M. capitata may be due in part to harboring a mixture of Cladocopium and Durusdinium spp., while P. acuta was dominated by other distinct Cladocopium spp., but there was no evidence of Symbiodiniaceae shuffling due to treatment or time. Only M. capitata survived the exposure and recovery period, but physiological state in heatwave-exposed M. capitata remained significantly diverged at the end of the recovery period relative to M. capitata that experienced ambient conditions. In extended heatwave and climate change stressor scenarios, our results indicate a species-specific loss of corals that are driven by baseline differences in both host and symbiont physiology. Notably, the species that survive climate change conditions exhibit lasting physiological legacies that are likely to influence future stress responses.