Widespread changes in temperature and precipitation patterns present plant species with new and combined stresses that affect their performance and distribution. Functional traits are indicators of plant resource use-acquisition strategies and thus they are commonly used to understand the geographic distributions of plant species and species’ potential responses to climate change. To date, most studies have targeted a few easy-to-measure leaf traits even though other traits, such as climatic tolerances, could provide valuable information directly related with species’ current and future distributions. Here, we measured both leaf functional traits and indices of physiological tolerance to heat (T50) and drought (Cell Membrane Stability) in 28 woody bamboo populations from 22 narrow-ranged species along a > 3000 m elevation gradient in the southern Peruvian Andes. We found that bamboo leaf functional traits remain fairly constant with a combination indicative of an acquisitive strategy (low leaf mass area and high nitrogen per mass) along the elevation gradient, despite drastic changes in environment and fast species turnover. Heat and drought tolerances of bamboos varied widely along the gradient and were negatively correlated to each other. Drought tolerance of bamboo populations was positively related with elevation and with precipitation seasonality while heat tolerance decreased at higher, colder elevations. When analyzed for individuals within each species or for individuals within each elevation, the two metrics of climatic tolerances did not show a consistent relationship, contrasting with the expectation of a potential trade-off between heat and drought tolerance. We also found that the measured leaf functional traits were not good predictors of climatic tolerances. Our results illustrate the diversity and complexity of the relationships between functional strategies and environmental gradients and highlight the limitations of using basic (i.e., “soft”) leaf traits to understand plant distributions and climatic tolerances.