We evaluate how hotspots of different types of extreme summertime heat change under global warming increase of up to 4∘C\documentclass[12pt]{minimal}
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\begin{document}$$4\,^\circ \hbox {C}$$\end{document}; and which level of global warming allows us to avert the risk of these hotspots considering the irreducible range of possibilities defined by well-sampled internal variability. We use large samples of low-probability extremes simulated by the 100-member Max Planck Institute Grand Ensemble (MPI-GE) for five metrics of extreme heat: maximum absolute temperatures, return periods of extreme temperatures, maximum temperature variability, sustained tropical nights, and wet bulb temperatures. At 2∘C\documentclass[12pt]{minimal}
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\begin{document}$$2\,^\circ \hbox {C}$$\end{document} of warming, MPI-GE projects maximum summer temperatures below 50∘C\documentclass[12pt]{minimal}
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\begin{document}$$50\,^\circ \hbox {C}$$\end{document} over most of the world. Beyond 2∘C\documentclass[12pt]{minimal}
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\begin{document}$$2\,^\circ \hbox {C}$$\end{document}, this threshold is overshot in all continents, with the maximum projected temperatures in hotspots over the Arabic Peninsula. Extreme 1-in-100-years pre-industrial temperatures occur every 10–25 years already at 1.5∘C\documentclass[12pt]{minimal}
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\begin{document}$$1.5\,^\circ \hbox {C}$$\end{document} of warming. At 4∘C\documentclass[12pt]{minimal}
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\begin{document}$$4\,^\circ \hbox {C}$$\end{document}, these 1-in-100-years extremes are projected to occur every 1 to 2 years over most of the world. The range of maximum temperature variability increases by 10–50% at 2∘C\documentclass[12pt]{minimal}
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\begin{document}$$2\,^\circ \hbox {C}$$\end{document} of warming, and by 50–100% at 4∘C\documentclass[12pt]{minimal}
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\begin{document}$$4\,^\circ \hbox {C}$$\end{document}. Beyond 2∘C\documentclass[12pt]{minimal}
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\begin{document}$$2\,^\circ \hbox {C}$$\end{document}, heat stress is aggravated substantially over non-adapted areas by hot and humid conditions that occur rarely in a pre-industrial climate; while extreme pre-industrial tropical night conditions become common-pace already at 1.5∘C\documentclass[12pt]{minimal}
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\begin{document}$$1.5\,^\circ \hbox {C}$$\end{document}. At 4∘C\documentclass[12pt]{minimal}
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\begin{document}$$4\,^\circ \hbox {C}$$\end{document} of warming, tropical night hotspots spread polewards globally, and are sustained during more than 99% of all summer months in the tropics; whilst extreme monthly mean wet bulb temperatures beyond 26∘C\documentclass[12pt]{minimal}
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\begin{document}$$26\,^\circ \hbox {C}$$\end{document} spread both over large tropical as well as mid-latitude regions.
