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Multiple recent record-shattering weather events raise questions about the adequacy of climate models to effectively predict and prepare for unprecedented climate impacts on human life, infrastructure, and ecosystems. Here, we show that extreme heat in several regions globally is increasing significantly and faster in magnitude than what state-of-the-art climate models have predicted under present warming even after accounting for their regional summer background warming. Across all global land area, models underestimate positive trends exceeding 0.5 °C per decade in widening of the upper tail of extreme surface temperature distributions by a factor of four compared to reanalysis data and exhibit a lower fraction of significantly increasing trends overall. To a lesser degree, models also underestimate observed strong trends of contraction of the upper tails in some areas, while moderate trends are well reproduced in a global perspective. Our results highlight the need to better understand and model the drivers of extreme heat and to rapidly mitigate greenhouse gas emissions to avoid further harm from unexpected weather events.