By increasing the mean and variance of environmental temperatures, climate change has caused local extinctions and range shifts of numerous species. However, biologists disagree on which populations and species are most vulnerable to future warming. This debate arises because biologists do not know which physiological processes are most vulnerable to temperature or how to model these processes in complex environments. Using the South American locust (Schistocerca cancellata) as a model system, my dissertation addressed this debate and explained how climate limits the persistence of locust populations. Locusts of S. cancellata are serious agricultural pests with occasional outbreaks covering up to 4 million km2 over six countries. Because outbreaks are largely driven by climate, understanding how climate limits the persistence of locusts may help predict crop losses in future climates. To achieve this aim, I integrated observational, experimental, and computational approaches. First, I tested a physiological model of heat stress. By measuring the heat tolerance of locusts under different oxygen concentrations, I demonstrated that heat tolerance depends on oxygen supply during the hatchling stage only. Second, I modeled the geographic distribution of locusts using physiological traits. I started by measuring thermal effects on consumption and defecation of field-captured locusts, and I then used these data to model energy gain in current and future climates. My results indicated that incorporating physiological mechanisms can improve the accuracy of models and alter predicted impacts of climate change. Finally, I explored the causes and consequences of intraspecific variation in heat tolerance. After measuring heat tolerance of locusts in different hydration states and developmental stages, I modeled survival in historical microclimates. My models indicated that recent climate change has amplified the risk of overheating for locusts, and this risk depended strongly on shade availability, hydration state, and developmental stage. Therefore, the survival of locusts in future climates will likely depend on their access to shade and water. Overall, my dissertation argues that modeling physiological mechanisms can improve the ability of biologists to predict the impacts of climate change.