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The propagation of drought from meteorological drought to soil moisture drought can be accelerated by high temperatures during dry periods. The occurrence of extremely long-duration dry periods in combination with extremely high temperatures may drive larger soil moisture deficits than either extreme occurring alone, and lead to severe impacts. In this study, we propose a framework to both characterise long-duration meteorological droughts that co-occur with extremely high temperatures and quantify their probability. We term these events as long-duration, dry and hot (DH) events and characterise them by their duration (D) and magnitude (M). D is defined as the consecutive number of days with precipitation below 1 mm, while M is the maximum daily maximum temperature during an event. A copula-based approach is then employed to estimate the probability of DH events. The framework is applied to Europe during the summer months of June, July and August. We also assess the change in probability that has occurred over the historical period 1950-2013 and find an increased probability of DH events throughout Europe where rising temperatures are found to be the main driver of this change. Dry periods are becoming hotter, leading to an increase in the occurrence of long-duration dry periods with extremely high temperatures. Some parts of Europe also show an increased probability of long-duration events although the relative change is not as strong as that seen with temperature. The results point to a predominant thermodynamic response of DH events to global warming and reaffirm previous research that soil moisture drought events are setting in faster and becoming more severe due to a change in the contributing meteorological hazards. It is hoped that the framework applied here will provide a starting point for further analysis of DH events in other locations and for the assessment of climate models.