Established forests currently function as a major carbon sink, sequestering as woody biomass about 26% of global fossil fuel emissions. Whether forests continue to act as a global sink will depend on many factors, including the response of aboveground wood production (AWP; MgC ha−1 yr−1) to climate change. Here, we explore how AWP in New Zealand's natural forests is likely to change. We start by statistically modelling the present-day growth of 97 199 individual trees within 1070 permanently marked inventory plots as a function of tree size, competitive neighbourhood and climate. We then use these growth models to identify the factors that most influence present-day AWP and to predict responses to medium-term climate change under different assumptions. We find that if the composition and structure of New Zealand's forests were to remain unchanged over the next 30 years, then AWP would increase by 6–23%, primarily as a result of physiological responses to warmer temperatures (with no appreciable effect of changing rainfall). However, if warmth-requiring trees were able to migrate into currently cooler areas and if denser canopies were able to form, then a different AWP response is likely: forests growing in the cool mountain environments would show a 30% increase in AWP, while those in the lowland would hardly respond (on average, −3% when mean annual temperature exceeds 8.0 °C). We conclude that response of wood production to anthropogenic climate change is not only dependent on the physiological responses of individual trees, but is highly contingent on whether forests adjust in composition and structure.