Thermal Performance Curves (TPCs) have become a popular tool for assessing the risk that climate warming and variability pose for species. These assessments typically rely upon measures of the match between a TPC and a population’s environment that doesn’t account for the outsized impact that stressful events such as heat waves can have on populations. To better capture the impact of short-term, but potentially catastrophic events, requires a better integration of environmental variation into population dynamic models. In this talk, I discuss a series of recent projects comprising both models and microcosm experiments, that are leading us toward a generalized representation of temperature-dependent population dynamics. I use methods from stochastic calculus to derive a simple metric of extinction risk under idealized assumptions and demonstrate the continued utility of this metric for predicting extinction risk in thermally varying environments.