Recent temperature extremes have shattered previously observed records, reaching intensities that were inconceivable before the events. Could the possibility of an event with such unprecedented intensity as the 2021 Pacific Northwest heatwave have been foreseen, based on climate model information available before the event? Could the scientific community have quantified its potential intensity based on the current generation of climate models? Here, we demonstrate how an ensemble boosting approach can be used to generate physically plausible storylines of a heatwave hotter than observed in the Pacific Northwest. We also show that heatwaves of much greater intensities than ever observed are possible in other locations like the Greater Chicago and Paris regions. In order to establish confidence in storylines of ‘black swan’-type events, different lines of evidence need to be combined along with process understanding to make this information robust and actionable for stakeholders.