Tropical mountains harbor globally significant levels of biodiversity and endemism. Climate change threatens many tropical montane species, yet little research has assessed the effects of climate change on the demographic rates of tropical species, particularly in the Afrotropics. Here, we report on the demographic rates of 21 Afrotropical bird species over 30 years in montane forests in Tanzania. We used mark–recapture analyses to model rates of population growth, recruitment, and apparent survival as functions of annual mean temperature and annual precipitation. For over one‐half of focal species, decreasing population growth rates were associated with increasing temperature. Due to the trend in temperature over time, we substituted a time covariate for the temperature covariate in top‐ranked population growth rate models. Temperature was a better explanatory covariate than time for 6 of the 12 species, or 29% of all focal species. Population growth rates were also lower for species found further below their elevational midpoint and for smaller‐bodied species. Changes in population growth rates were more closely tied to changes in recruitment than to changes in apparent survival. There were no consistent associations between demographic rates and precipitation. This study demonstrates temperature‐associated demographic impacts for 6 (29%) of 21 focal species in an Afrotropical understory bird community and highlights the need to incorporate the impacts of climate change on demographic rates into conservation planning across the tropics.