Natural populations evolve in unpredictable environments where rare and devastating events such as drought, fire, and starvation pose the risk of extinction. Episodes of severe stress are presumed to underlie traits like plasticity and bet-hedging, that help mitigate environmental risk. In this study we experimentally evolved yeast populations in an environment characterized by intermittent episodes of heat-induced stress. Stress events initially killed nearly 99% of the population. However, after 400 generations all experimental populations had evolved significantly reduced mortality rates, along with a reduction in the time taken to recover after heat shock. More notably, stress-adapted populations also showed significantly reduced rates of growth in benign conditions relative to the ancestral strain. Indeed, a tradeoff between growth rate and stress tolerance is predicted from prior work on the yeast stress response, which shows that reduced growth, regardless of its cause, is correlated with increased stress resistance. To dissect the various components of fitness in our experimental regime, we collected time-lapse microscopy data on thousands of individual cells during exponential growth and heat shock. We show that the time-averaged geometric mean fitness of stress-adapted populations is far greater than the ancestor, despite the short-term cost of reducing growth during favorable conditions. Still, these results imply the establishment and fixation of mutations that reduce fitness at all times except during the brief instance of heat stress. We are currently investigating the dynamics of adaptive mutations arising in our experiment using whole-genome whole-population sequencing from time points across the evolution experiment. Taken together, our results support the classical prediction that selection in variable environments acts to increase geometric mean fitness, but also highlight evolutionary constraints that arise in environments where the fitness effects of a mutation are variable across time.