The attribution of extreme events typically focuses on individual events, such as heatwaves. In our study, we extend this approach to include complete time series during such events in order to capture their temporal dependence. Using today's knowledge, we find that the influence of anthropogenic greenhouse gas emissions on heatwaves could already have been proven in the 1960s. It is very likely that 21st-century heatwaves over Europe would be impossible without these emissions.