Following the adoption of the Paris Agreement, there has been an increasing interest in quantifying impacts at discrete levels of global mean temperature (GMT) increase such as 1.5 °C and 2 °C above pre-industrial levels. Consequences of anthropogenic greenhouse gas emissions on agricultural productivity have direct and immediate relevance for human societies. Future crop yields will be affected by anthropogenic climate change as well as direct effects of emissions such as CO2 fertilization. At the same time, the climate sensitivity to future emissions is uncertain. Here we investigate the sensitivity of future crop yield projections with a set of global gridded crop models for four major staple crops at 1.5 °C and 2 °C warming above pre-industrial levels, as well as at different CO2 levels determined by similar probabilities to lead to 1.5 °C and 2 °C, using climate forcing data from the Half a degree Additional warming, Prognosis and Projected Impacts project. For the same CO2 forcing, we find consistent negative effects of half a degree warming on productivity in most world regions. Increasing CO2 concentrations consistent with these warming levels have potentially stronger but highly uncertain effects than 0.5 °C warming increments. Half a degree warming will also lead to more extreme low yields, in particular over tropical regions. Our results indicate that GMT change alone is insufficient to determine future impacts on crop productivity.