The overwhelming majority of integrated assessments of future climate risks are made using climate scenarios and projections superimposed on current socio-economic conditions only; hence they fail to account for the influence of socio-economic changes. Following the recent IPCC-related new scenarios framework for climate change research, a few assessments of climate risks have attempted to integrate socio-economic changes through the combination of climate and socio-economic scenarios. However, a number of shortcomings remain, such as the lack of consideration of vulnerability, the low spatial resolution, and the lack of contextual focus. In this paper, we seek to examine these shortcomings through an exploratory assessment of future heat stress risk in 271 European regions up to 2030, based on the combination of several climate (representative concentration pathways - RCPs) and socio-economic (Shared socioeconomic pathways - SSPs) scenarios. We also discuss the main barriers faced – such as the availability of socio-economic projections and the diversity of existing socio-economic scenarios – and provide a reflection on promising approaches to foster the use of socio-economic projections and scenarios within integrated assessments of future climate risks.