Heatwaves have become more common and severe due to climate change, especially rising temperatures, posing a serious public health problem in tropical countries. In this paper, a modified version of the Heat–SEIR model is developed to investigate the influence of seasonal temperature changes and long-term warming on population health. This model was developed by incorporating temperature-related parameters in the classical SEIR model. Seasonal and long-term temperature changes were modeled as a bounded sinusoidal function using average temperature data for Bangladesh from 2000 to 2024. Firstly, the mathematical properties of the proposed model were investigated, and its positivity and boundedness were proved. Then the disease-free equilibrium and the basic reproduction number R₀ were derived. From the local stability analysis of the proposed model, the disease-free equilibrium was stable if R₀ < 1 and unstable if R₀ > 1. However, the existence of the endemic equilibrium when R₀ > 1 was been proved.

Furthermore, the influence of temperature change was investigated using the Pearson correlation coefficient between the maximum temperature and other climate-related parameters. Sensitivity analysis was also conducted using normalized sensitivity indices and partial rank correlation coefficients to identify the parameters that most influence the proposed model. From the sensitivity analysis, the transmission and recovery rates were identified, as well as the most influential parameters, while heat-related mortality and temperature-sensitivity parameters were also found to influence the proposed model to a certain extent. Conducting a simulation to demonstrate the effects of seasonal heatwaves and long-term warming on population health, this study provides a clear, data-driven modeling framework for understanding heat-related health risks and could inform future public health planning.