Projecting the impacts of climate change on agriculture requires knowing or assuming how farmers will adapt. But empirical estimates of the effectiveness of this private adaptation are scarce and the sensitivity of impact assessments to adaptation assumptions is not well understood. Here we assess the potential effectiveness of private farmer adaptation in Europe by jointly estimating both short-run and long-run response functions using time-series and cross-sectional variation in subnational yield and profit data. The difference between the impacts of climate change projected using the short-run (limited adaptation) and long-run (substantial adaptation) response curves can be interpreted as the private adaptation potential. We find high adaptation potential for maize to future warming but large negative effects and only limited adaptation potential for wheat and barley. Overall, agricultural profits could increase slightly under climate change if farmers adapt but could decrease in many areas if there is no adaptation. Decomposing the variance in 2040 projected yields and farm profits using an ensemble of 13 climate model-runs, we find that the rate at which farmers will adapt to rising temperatures is an important source of uncertainty.