Despite their fundamental importance the links between forest productivity, diversity and climate remain contentious. We consider whether variation in productivity across climates reflects adjustment among tree species and individuals, or changes in tree community structure. We analysed data from 60 plots of humid old-growth forests spanning mean annual temperatures (MAT) from 2.0 to 26.6 °C. Comparing forests at equivalent aboveground biomass (160 Mg C ha-1), tropical forests ≥24 °C MAT averaged more than double the aboveground woody productivity of forests <12 °C (3.7 ± 0.3 versus 1.6 ± 0.1 Mg C ha-1 yr-1). Nonetheless, species with similar standing biomass and maximum stature had similar productivity across plots regardless of temperature. We find that differences in the relative contribution of smaller- and larger-biomass species explained 86% of the observed productivity differences. Species-rich tropical forests are more productive than other forests due to the high relative productivity of many short-stature, small-biomass species.