Species migration in response to warming temperatures is expected to lead to ‘biotic attrition,’ or loss of local diversity, in areas where the number of species emigrating or going locally extinct exceeds the number immigrating. Biotic attrition is predicted be especially severe in the low-lying hot tropics since elevated temperatures may surpass the observed tolerances of most extant species. It is possible, however, that the estimated temperature niches of many species are inaccurate and truncated with respect to their true tolerances due to the absence of hotter areas under current global climate. If so, these species will be capable of persisting in some areas where future temperatures exceed current temperatures, reducing rates of biotic attrition. Here, we use natural history collections data to estimate the realized thermal niches of > 2000 plant species from the tropical forests of South America. In accord with the truncation hypothesis, we find that the thermal niches of species from hot lowland areas are several degrees narrower than the thermal niches of species from cooler areas. We estimate rates of biotic attrition for South American tropical forests due to temperature increases ranging from 1 to 5 °C, and under two niche assumptions. The first is that the observed thermal niches truly reflect the plant's tolerances and that the reduction in niche breadth is due to increased specialization. The second is that lowland species have the same mean thermal niche breadth as nonlowland and nonequatorial species. The differences between these two models are dramatic. For example, using observed thermal niches we predict an almost complete loss of plant diversity in most South American tropical forests due to a 5 °C temperature increase, but correcting for possible niche truncation we estimate that most forests will retain > 50–70% of their current species richness. The different predictions highlight the importance of using fundamental vs. realized niches in predicting the responses of species to global climate change.