Climate model based storylines of individual climate and weather events are increasingly used to quantify impacts, vulnerability, or stress-test infrastructure to inform adaptation decisions. Here, we present an approach to test the plausibility of unprecedented climate storylines based on physical conformity, internal consistency, and historical precedent. We apply this approach to assess the plausibility of month-long heatwaves in Western Europe that would exceed existing record temperatures by around 5 K. These heatwaves are based on model simulations using ensemble boosting, a computationally efficient method to simulate unprecedented events. We compare these unprecedented heatwaves with historical heatwaves in a reanalysis data set, using standardised anomalies relative to a time-evolving climatology of relevant physical variables such as temperature, 500 hPa geopotential height, surface solar radiation, and soil moisture. We show that these unprecedented heatwaves are associated with physical drivers similar to historical heatwaves, with anomalies that are more intense in magnitude but very similar in their temporal substructure. We also demonstrate that the relationships between different physical variables are internally consistent and exhibit many similarities with historical precedents. In this way, we show that these unprecedented long-lasting heatwaves cannot be ruled out as implausible, and thus highlight the need to anticipate such events when planning adaptation measures. Similar approaches can be used to assess the plausibility of unprecedented events in other variables.