Public health is threatened by climate change and extreme temperature events worldwide. Differences in health predispositions, access to cooling infrastructure and occupation raises an issue of heat-related health inequality in those vulnerable and disadvantaged demographic groups. To address these issues, a comprehensive understanding of the effect of elevated body temperatures on human biological systems and overall health is urgently needed. In this paper we look at the inner workings of the human innate immunity under exposure to heat stress induced through exposure to environment and physical exertion. We couple two experimentally validated computational models: the innate immune system and thermal regulation of the human body. We first study the dynamics of critical indicators of innate immunity as a function of human core temperature. Next, we identify environmental and physical activity regimes that lead to core temperature levels that can potentially compromise the performance of the human innate immunity. Finally, to take into account the response of innate immunity to various intensities of physical activities, we utilise the dynamic core temperatures generated by a thermal regulation model. We compare the dynamics of all key players of the innate immunity for a variety of stresses like running a marathon, doing construction work, and leisure walking at speed of 4 km/h, all in the setting of a hot and humid tropical climate such as present in Singapore. We find that exposure to moderate heat stress leading to core temperatures within the mild febrile range (37, 38][Formula: see text], nudges the innate immune system into activation and improves the efficiency of its response. Overheating corresponding to core temperatures beyond 38[Formula: see text], however, has detrimental effects on the performance of the innate immune system, as it further induces inflammation, which causes a series of reactions that may lead to the non-resolution of the ongoing inflammation. Among the three physical activities considered in our simulated scenarios (marathon, construction work, and walking), marathon induces the highest level of inflammation that challenges the innate immune response with its resolution. Our study advances the current state of research towards understanding the implications of heat exposure for such an essential physiological system as the innate immunity. Although we find that among considered physical activities, a marathon of 2 h and 46 min induces the highest level of inflammation, it must be noted that construction work done on a daily basis under the hot and humid tropical climate, can produce a continuous level of inflammation triggering moieties stretched at a longer timeline beating the negative effects of running a marathon. Our study demonstrates that the performance of the innate immune system can be severely compromised by the exposure to heat stress and physical exertion. This poses significant risks to health especially to those with limited access to cooling infrastructures. This is due in part to having low income, or having to work on outdoor settings, which is the case for construction workers. These risks to public health should be addressed through individual and population-level measures via behavioural adaptation and provision of the cooling infrastructure in outdoor environments.