Rising temperatures due to climate change influence the wood production of forests. Observations show that some temperate forests increase their productivity, whereas others reduce their productivity. This study focuses on how species composition and forest structure properties influence the temperature sensitivity of aboveground wood production (AWP). It further investigates which forests will increase their productivity the most with rising temperatures. We described forest structure by leaf area index, forest height and tree height heterogeneity. Species composition was described by a functional diversity index (Rao's Q) and a species distribution index (ΩAWP). ΩAWP quantified how well species are distributed over the different forest layers with regard to AWP. We analysed 370 170 forest stands generated with a forest gap model. These forest stands covered a wide range of possible forest types. For each stand, we estimated annual aboveground wood production and performed a climate sensitivity analysis based on 320 different climate time series (of 1-year length). The scenarios differed in mean annual temperature and annual temperature amplitude. Temperature sensitivity of wood production was quantified as the relative change in productivity resulting from a 1 ∘C rise in mean annual temperature or annual temperature amplitude. Increasing ΩAWP positively influenced both temperature sensitivity indices of forest, whereas forest height showed a bell-shaped relationship with both indices. Further, we found forests in each successional stage that are positively affected by temperature rise. For such forests, large ΩAWP values were important. In the case of young forests, low functional diversity and small tree height heterogeneity were associated with a positive effect of temperature on wood production. During later successional stages, higher species diversity and larger tree height heterogeneity were an advantage. To achieve such a development, one could plant below the closed canopy of even-aged, pioneer trees a climax-species-rich understorey that will build the canopy of the mature forest. This study highlights that forest structure and species composition are both relevant for understanding the temperature sensitivity of wood production.