In June 2021, the Pacific Northwest experienced a heatwave that broke all previous records. Estimated return levels based on observations up to the year before the event suggested that reaching such high temperatures is not possible in today's climate. We here assess the suitability of the prevalent statistical approach by analyzing extreme temperature events in climate model large ensemble and synthetic extreme value data. We demonstrate that the method is subject to biases, as high return levels are generally underestimated and, correspondingly, the return period of low‐likelihood heatwave events is overestimated, if the underlying extreme value distribution is derived from a short historical record. These biases have even increased in recent decades due to the emergence of a pronounced climate change signal. Furthermore, if the analysis is triggered by an extreme event, the implicit selection bias affects the likelihood assessment depending on whether the event is included in the modeling.