Rapid warming and high temperatures are an immediate threat to global ecosystems, but the threat may be especially pronounced in the tropics. Although low‐latitude tree species are widely predicted to be vulnerable to warming, information about how tropical tree diversity and community composition respond to elevated temperatures remains sparse. Here, we study long‐term responses of tree diversity and composition to increased soil and air temperatures at the Boiling River—an exceptional and unique “natural warming experiment” in the central Peruvian Amazon. Along the Boiling River's course, geothermally heated water joins the river, gradually increasing water temperature and subsequently warming the surrounding forest. In the riparian forests along the Boiling River, mean annual and maximum air temperatures span gradients of 4°C and 11°C, respectively, over extremely short distances (< 1 km), with the hottest temperatures matching those predicted for much of the Amazon under future global warming scenarios. Using a new network of 70 woody plant inventory plots situated along the Boiling River's thermal gradient, we observed a ca. 11% decline in tree α‐diversity per 1°C increase in mean annual temperature. We also found that the tree communities growing under elevated temperatures were generally more thermophilic (i.e., included greater relative abundances of species from hotter parts of the Amazon) than the communities in cooler parts of the gradient. Based on patterns at the Boiling River, we hypothesize that global warming will lead to dramatic shifts in tree diversity and composition in the lowland Amazon, including local extinctions and biotic attrition.