Rain forest has been a persistent feature in South America for ≥55 million years. However, climate-envelope models predict that future air temperature increases will cause pervasive tree species extinction, and some biosphere models predict widespread Amazon forest die-off. We used a phylogeographic analysis to estimate the age of 12 widespread Amazon tree species to determine if they have persisted though times when air temperatures were similar to predicted levels over the coming decades. Nine of the 12 study species originated >2.6 Ma ago when air temperatures were warmer than today, and may have been similar to 2100 projections under mid-range anthropogenic emissions scenarios. Our results suggest that, all else being equal, near-term high temperature induced Amazon tree species extinction is unlikely.