Thermal performance curves enable physiological constraints to be incorporated in predictions of biological responses to shifts in mean temperature. But do thermal performance curves adequately capture the biological impacts of thermal extremes? Organisms incur physiological damage during exposure to extremes, and also mount active compensatory responses leading to acclimatization, both of which alter thermal performance curves and determine the impact that current and future extremes have on organismal performance and fitness. Thus, these sub-lethal responses to extreme temperatures potentially shape evolution of thermal performance curves. We applied a quantitative genetic model and found that beneficial acclimatization and cumulative damage alter the extent to which thermal performance curves evolve in response to thermal extremes. The impacts of extremes on the evolution of thermal performance curves are reduced if extremes cause substantial mortality or otherwise reduce fitness differences among individuals. Further empirical research will be required to understand how responses to extremes aggregate through time and vary across life stages and processes. Such research will enable incorporating passive and active responses to sub-lethal stress when predicting the impacts of thermal extremes.