Evolutionary adaptation may be vital for the persistence of ectothermic species under climate change. Increases in both the mean and variability of environmental temperature are occurring, and each of these variables may act as agents of selection on different traits that may not be heritable or have the capacity to evolve independently from one another. If the ‘baseline’ values of thermal performance traits cannot evolve, phenotypic plasticity driven by gene expression might become critical. We review the literature for evidence that thermal performance traits in ectotherms are heritable and have genetic architectures that permit their unconstrained evolution. Next, we examine the relationship between gene expression and both the magnitude and duration of thermal stress. We find that evolution in many species appears to be constrained by genetic correlations such that populations can adapt to either increases in mean temperature or temperature variability, but not both. Nevertheless, there is rampant capacity for plastic expression of the transcriptome in response to temperature shifts, with the number of differentially expressed genes increasing with the magnitude, but not the duration, of thermal stress. We use these observations to develop a conceptual model that describes how evolution is likely to progress as the climate continues to change. We argue that extreme weather events, rather than gradual increases in mean temperature, are more likely to drive genetic and phenotypic change in wild ectotherms.