Species’ distributions will respond to climate change based on the relationship between local demographic processes and climate and how this relationship varies based on range position. A rarely tested demographic prediction is that populations at the extremes of a species’ climate envelope (e.g., populations in areas with the highest mean annual temperature) will be most sensitive to local shifts in climate (i.e., warming). We tested this prediction using a dynamic species distribution model linking demographic rates to variation in temperature and precipitation for wood frogs (Lithobates sylvaticus) in North America. Using long-term monitoring data from 746 populations in 27 study areas, we determined how climatic variation affected population growth rates and how these relationships varied with respect to long-term climate. Some models supported the predicted pattern, with negative effects of extreme summer temperatures in hotter areas and positive effects on recruitment for summer water availability in drier areas. We also found evidence of interacting temperature and precipitation influencing population size, such as extreme heat having less of a negative effect in wetter areas. Other results were contrary to predictions, such as positive effects of summer water availability in wetter parts of the range and positive responses to winter warming especially in milder areas. In general, we found wood frogs were more sensitive to changes in temperature or temperature interacting with precipitation than to changes in precipitation alone. Our results suggest that sensitivity to changes in climate cannot be predicted simply by knowing locations within the species’ climate envelope. Many climate processes did not affect population growth rates in the predicted direction based on range position. Processes such as species-interactions, local adaptation, and interactions with the physical landscape likely affect the responses we observed. Our work highlights the need to measure demographic responses to changing climate.