Summary Given the contrasting short‐term temperature dependences of gross primary production (GPP) and autotrophic respiration, the fraction of GPP respired by trees is predicted to increase with warming, providing a positive feedback to climate change. However, physiological acclimation may dampen or eliminate this response. We measured the fluxes of aboveground respiration (Ra), GPP and their ratio (Ra/GPP) in large, field‐grown Eucalyptus tereticornis trees exposed to ambient or warmed air temperatures (+3°C). We report continuous measurements of whole‐canopy CO2 exchange, direct temperature response curves of leaf and canopy respiration, leaf and branch wood respiration, and diurnal photosynthetic measurements. Warming reduced photosynthesis, whereas physiological acclimation prevented a coincident increase in Ra. Ambient and warmed trees had a common nonlinear relationship between the fraction of GPP that was respired above ground (Ra/GPP) and the mean daily temperature. Thus, warming significantly increased Ra/GPP by moving plants to higher positions on the shared Ra/GPP vs daily temperature relationship, but this effect was modest and only notable during hot conditions. Despite the physiological acclimation of autotrophic respiration to warming, increases in temperature and the frequency of heat waves may modestly increase tree Ra/GPP, contributing to a positive feedback between climate warming and atmospheric CO2 accumulation.