Daily minimum temperature (Tmin) is increasing faster than maximum temperature. However its impact on the physiology of crop yield and adaptation is barely studied. Using 42 years of annual yield trials at 255 sites representing most spring wheat production regions, the effects of environmental covariates were examined. During grainfilling, average Tmin explained 40% of yield variation, and 52% considering radiation; generally an increase of 1 degree C reduces yield ~0.5 t/ha. The relation between yield was linear over a 14 degree C range. An average increase of 1.2 degree C at the test sites reduced yield by more than 10%. A shortened grainfilling period is part of the explanation; nocturnal rates of dark respiration are also likely factors. Improvement of adaptation to warmer nights could generate a step-change in wheat yield, the most widely-grown crop globally, covering more than 220 million ha, and providing 20% of human calories and protein. ### Competing Interest Statement The authors have declared no competing interest. Digital Transformation and the Climate Action Science Programs of CGIAR International Wheat Yield Partnership (IWYP) funded by the Biotechnology and Biological Research Council of the UK

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