Species are predicted to shift their distributions upslope or poleward in response to global warming. This prediction is supported by a growing number of studies documenting species migrations in temperate systems but remains poorly tested for tropical species, and especially for tropical plant species. We analyzed changes in tree species composition in a network of 10 annually censused 1-ha plots spanning an altitudinal gradient of 70–2800 m elevation in Costa Rica. Specifically, we combined plot data with herbarium records (accessed through GBIF) to test if the plots' community temperature scores (CTS, average thermal mean of constituent species weighted by basal area) have increased over the past decade as is predicted by climate-driven species migrations. In addition, we quantified the contributions of stem growth, recruitment, and mortality to the observed patterns. Supporting our a priori hypothesis of upward species migrations, we found that there have been consistent directional shifts in the composition of the plots, such that the relative abundance of lowland species, and hence CTS, increased in 90% of plots. The rate of the observed compositional shifts corresponds to a mean thermal migration rate (TMR) of 0.0065 °C yr−1 (95% CI = 0.0005–0.0132 °C yr−1). While the overall TMR is slower than predicted based on concurrent regional warming of 0.0167 °C yr−1, migrations were on pace with warming in 4 of the 10 plots. The observed shifts in composition were driven primarily by mortality events (i.e., the disproportionate death of highland vs. lowland species), suggesting that individuals of many tropical tree species will not be able to tolerate future warming and thus their persistence in the face of climate change will depend on successful migrations. Unfortunately, in Costa Rica and elsewhere, land area inevitably decreases at higher elevations; hence, even species that are able to migrate successfully will face heightened risks of extinction.