Cities are facing increased heat-related health risks (HHRs) due to the combined effects of global warming and rapid urbanization. However, few studies have focused on HHR assessment based on fine-scale information. Moreover, most studies only analyze spatial HHR patterns and do not explore the potential driving factors. In this study, we estimated the potential HHRs based on the “hazard–exposure–vulnerability” framework by using multisource data, including the modified thermal–humidity index (MTHI), population density, and land cover. Then, the variations in the HHRs among different local climate zones (LCZs) at the fine spatial scale were analyzed in detail. Finally, we compared the different contributions of the LCZs and types of land cover to the HHRs and their three components by using multiple linear regression models. The results indicate that the spatial pattern of the HHRs was different from those of the individual components, and high-hazard regions do not mean high HHRs. There were huge variations in the HHRs among the different LCZs. The built-up LCZs typically had much higher HHRs than the natural ones, with compact LCZs facing the most severe risk. LCZ 6 (open low-rise buildings) had a relatively low HHR and should be paid more attention in future urban planning. Compared to the LCZs, the land covers better explained the variations in the HHR. In contrast, the LCZs better predicted the land surface temperatures. However, both the LCZs and land covers made only slight contributions to the heat exposure and vulnerability. Furthermore, the manmade buildings and impervious surface areas contributed much more to the HHR than the natural land covers. Therefore, the arrangement of the warming LCZs and land cover types is worthy of further investigation from the perspective of HHR mitigation.