Understanding how annual climate variation affects population growth rates across a species’ range may help us anticipate the effects of climate change on species distribution and abundance. We predict that populations in warmer or wetter parts of a species’ range should respond negatively to periods of above average temperature or precipitation, respectively, whereas populations in colder or drier areas should respond positively to periods of above average temperature or precipitation. To test this, we estimated the population sensitivity of a common shrub species, big sagebrush (Artemisia tridentata), to annual climate variation across its range. Our analysis includes 8,175 observations of year‐to‐year change in sagebrush cover or production from 131 monitoring sites in western North America. We coupled these observations with seasonal weather data for each site and analyzed the effects of spring through fall temperatures and fall through spring accumulated precipitation on annual changes in sagebrush abundance. Sensitivity to annual temperature variation supported our hypothesis: years with above average temperatures were beneficial to sagebrush in colder locations and detrimental to sagebrush in hotter locations. In contrast, sensitivity to precipitation did not change significantly across the distribution of sagebrush. This pattern of responses suggests that regional abundance of this species may be more limited by temperature than by precipitation. We also found important differences in how the ecologically distinct subspecies of sagebrush responded to the effects of precipitation and temperature. Our model predicts that a short‐term temperature increase could produce an increase in sagebrush cover at the cold edge of its range and a decrease in cover at the warm edge of its range. This prediction is qualitatively consistent with predictions from species distribution models for sagebrush based on spatial occurrence data, but it provides new mechanistic insight and helps estimate how much and how fast sagebrush cover may change within its range.