Extreme temperatures have reached unprecedented levels in many regions of the globe due to climate change anda further increase is expected. Besides other consequences, high temperatures increase the mortality risk and severely affectthe labour productivity of workers. We perform a high-resolution spatial analysis to assess the impacts of heat on mortality and labour productivity in Switzerland and project their development under different Representative Concentration Pathway (RCP) scenarios, considering that no socio-economic changes takes place. The model is based on the risk framework of the Intergovernmental Panel on Climate Change (IPCC), which combines the three risk components: Hazard, Exposure, and Vulnerability. We model the two impact categories in the same spatially explicit framework and we integrate uncertainties into the analysis through a Monte Carlo simulation. We model, that first, about 670 people die today per year because of heat in Switzerland. Second, the economic costs caused by losses in labour productivity amount to around CHF 413 million (approx. $ 465 million) per year. Should we remain on an RCP8.5 emissions pathway, these values may double (for mortality) or even triple (for labour productivity) by the end of the century. Under an RCP2.6 scenario impacts are expected to slightly increaseand peak around mid-century, when climate is assumed to stop warming. Even though uncertainties in the model are large, theunderlying trend in impacts is unequivocal. The results of the study are valuable information for political discussions and allowfor a better understanding of the cost of inaction.