Species are predicted to respond to global warming through ‘cold-ward’ shifts in their geographic distributions due to encroachment into newly suitable habitats and/or dieback in areas that become climatically unsuitable. I conduct one of the first-ever tests of this hypothesis for tropical plant species. I test for changes in the thermal distributions of 239 South American tropical plant species using dated herbarium records for specimens collected between 1970 and 2009. Supporting a priori predictions, many species (59%) exhibit some evidence of significant cold-ward range shifts even after correcting for collection biases. Over 1/3 of species (35%) show significant cold-ward movement in their hot thermal limits (mean rate of change = 0.022 °C yr−1). Most of these species (85%; 30% of all study species) show no corresponding shift in their cold thermal limits. These unbalanced changes in the species’ thermal range limits may indicate species that are experiencing dieback due to their intolerance of rising temperatures coupled with an inability to expand into newly climatically suitable habitats. On the other hand, 25% of species show significant cold-ward shifts in their cold thermal range limits (mean rate of change = 0.003 °C yr−1), but 80% of these species (20% of all study species) show no corresponding shift in their hot thermal range limits. In these cases, the unbalanced shifts may indicate species that are able to ‘benefit’ under global warming, at least temporally, by both tolerating rising temperatures and expanding into new suitable habitat. An important ancillary result of this study is that the number of species exhibiting significant range shifts was greatly influenced by shifting collector biases. This highlights the need to account for biases when analyzing natural history records or other long-term records.