Climate warming is expected to increase respiration rates of tropical forest trees and lianas, which may negatively affect the carbon balance of tropical forests. Thermal acclimation could mitigate the expected respiration increase, but the thermal acclimation potential of tropical forests remains largely unknown. In a tropical forest in Panama, we experimentally increased nighttime temperatures of upper canopy leaves of three tree and two liana species by on average 3 °C for 1 week, and quantified temperature responses of leaf dark respiration. Respiration at 25 °C (R25) decreased with increasing leaf temperature, but acclimation did not result in perfect homeostasis of respiration across temperatures. In contrast, Q10 of treatment and control leaves exhibited similarly high values (range 2.5–3.0) without evidence of acclimation. The decrease in R25 was not caused by respiratory substrate depletion, as warming did not reduce leaf carbohydrate concentration. To evaluate the wider implications of our experimental results, we simulated the carbon cycle of tropical latitudes (24°S–24°N) from 2000 to 2100 using a dynamic global vegetation model (LM3VN) modified to account for acclimation. Acclimation reduced the degree to which respiration increases with climate warming in the model relative to a no-acclimation scenario, leading to 21% greater increase in net primary productivity and 18% greater increase in biomass carbon storage over the 21st century. We conclude that leaf respiration of tropical forest plants can acclimate to nighttime warming, thereby reducing the magnitude of the positive feedback between climate change and the carbon cycle.