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 width of extreme surface temperature distributions by a factor of 4.1 compared to reanalysis data, and exhibit a lower fraction of significantly-increasing trends overall. This highlights 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.