Responses of global crop yields to warmer temperatures are fundamental to sustainable development under climate change but remain uncertain. Here, we combined a global dataset of field warming experiments (48 sites) for wheat, maize, rice and soybean with gridded global crop models to produce field-data-constrained estimates on responses of crop yield to changes in temperature (ST) with the emergent-constraint approach. Our constrained estimates show with >95% probability that warmer temperatures would reduce yields for maize (−7.1 ± 2.8% K−1), rice (−5.6 ± 2.0% K−1) and soybean (−10.6 ± 5.8% K−1). For wheat, ST was 89% likely to be negative (−2.9 ± 2.3% K−1). Uncertainties associated with modelled ST were reduced by 12–54% for the four crops but data constraints do not allow for further disentangling ST of different crop types. A key implication for impact assessments after the Paris Agreement is that direct warming impacts alone will reduce major crop yields by 3–13% under 2 K global warming without considering CO2 fertilization effects and adaptations. Even if warming was limited to 1.5 K, all major producing countries would still face notable warming-induced yield reduction. This yield loss could be partially offset by projected benefits from elevated CO2, whose magnitude remains uncertain, and highlights the challenge to compensate it by autonomous adaptation. Global responses of crops to warmer temperatures will affect agricultural sustainability. This study of maize, rice, soybean and wheat projects yield reductions of 3–13% under 2 °C warming.