Extreme heat undermines the working capacity of individuals, resulting in lower productivity, and thus economic output. Here we analyse the present and future economic damages due to reduced labour productivity caused by extreme heat in Europe. For the analysis of current impacts, we focused on heatwaves occurring in four recent anomalously hot years (2003, 2010, 2015, and 2018) and compared our findings to the historical period 1981-2010. In the selected years, the total estimated damages attributed to heatwaves amounted to 0.3-0.5% of European gross domestic product (GDP). However, the identified losses were largely heterogeneous across space, consistently showing GDP impacts beyond 1% in more vulnerable regions. Future projections indicate that by 2060 impacts might increase in Europe by a factor of almost five compared to the historical period 1981-2010 if no further mitigation or adaptation actions are taken, suggesting the presence of more pronounced effects in the regions where these damages are already acute.