Heat islands and ongoing urbanization make cities places where the negative impacts of global climate change on society are becoming increasingly evident. Especially the interplay and potential multiplication of heat, low green provision, and the presence of socially deprived urban dwellers constitutes complex challenges. Emerging climate injustices and potential health issues require a powerful counter-reaction in form of adaptation action. For our study, we consider eight cities located in the densely populated and historically highly segregated Ruhr area in Western Germany, which is one of the largest metropolitan areas in Europe with a heterogeneous distribution of socio-spatial problems, economic potential, heat stress, and green infrastructures. We use land surface temperature (LST), data on green provision (normalized difference vegetation index (NDVI)), and social indicators to reveal the relationships between these indicators on the city district level (n = 275). Therefore, we first analyze the data regarding spatial autocorrelation (Moran'sI) and clustering (Gi*) before calculating study area wide and city specific correlations between the three factors regarded. Finally, we conduct a cluster analysis (k-means) to disclose similar areas with or without multiple burdens. Our results show distinct disparities in heat exposure, green availability, and social status between city districts of the study area. We find strong negative correlations between LST and NDVI as well as between NDVI and social status. The relationship between LST and our social indicator remains ambiguous, affirming the necessity of further detailed studies. The cluster analysis furthermore allows for the visualization and classification of districts featuring similar characteristics regarding the researched components. We can discern in parts pronounced climate injustice in the studied cities, with a majority of people living in unfavorable environmental and socio-economic conditions. Our analysis supports governments and those responsible for urban planning in addressing climate injustice in the future.