Predicting the responses of forest growth to elevated temperature (T) and atmospheric CO2 concentration ([CO2]) on decadal time scales presents a formidable challenge because of the many interacting processes involved. A key uncertainty concerns the relative importance of plant and soil processes to the overall long-term response. In this study, the plant-soil model GDAY was used to simulate forest growth responses to T and [CO2] on different time scales for forests in cool and warm climates. An equilibrium-based graphical analysis was used to distinguish the roles played by plant and soil processes in determining the response. Doubled [CO2] caused a large initial increase (20%) in net primary productivity (NPP), but this did not persist in the long term. By contrast, a 2 degrees C increase in T caused a persistent long-term increase in NPP of approximately 10-15%. These responses were similar at cool and warm sites. The equilibrium analysis indicated that soil processes dominated the long-term responses predicted by the model. In particular, the predicted long-term increase in NPP under elevated T reflected an increase in predicted N mineralization and plant N uptake, assuming that a constant fraction of mineralized N is taken up by plants. The analysis highlights key uncertainties for future research.