Heatwaves are phenomena that have large social and economic consequences. Understanding and estimating the frequency of such events are of great importance to climate scientists and decision makers. Heatwaves are a type of extreme event which are by definition rare and as such there are few data in the historical record to help planners. Extreme value theory is a general framework from which inference can be drawn from extreme events. When modelling heatwaves it is important to take into account the intensity and duration of events above a critical level as well as the interaction between both factors. Most previous methods assume that the duration distribution is independent of the critical level that is used to define a heatwave: a shortcoming that can lead to incorrect inferences. The paper characterizes a novel method for analysing the temporal dependence of heatwaves with reference to observed temperatures from Orleans in central France. This method enables estimation of the probabilities for heatwave events irrespectively of whether the duration distribution is independent of the critical level. The methods are demonstrated by estimating the probability of an event more severe than the 2003 European heatwave or an event that causes a specified increase in mortality.