We evaluate how hotspots of different types of extreme summertime heat change under global warming increase of up to ; 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 of warming, MPI-GE projects maximum summer temperatures below over most of the world. Beyond , 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 of warming. At , 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 of warming, and by 50–100% at . Beyond , 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 . At 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 spread both over large tropical as well as mid-latitude regions.