Climate change-derived extreme heat phenomena are one of the major concerns across the globe, including Bangladesh. The appraisal of historical spatiotemporal changes and possible future changes in heat index (HI) is essential for developing heat stress mitigation strategies. However, the climate-health nexus studies in Bangladesh are very limited. This study was intended to appraise the historical and projected changes in HI in Bangladesh. The HI was computed from daily dry bulb temperature and relative humidity. The modified Mann-Kendal (MMK) test and linear regression were used to detect trends in HI for the observed period (1985-2015). The future change in HI was projected for the mid-century (2041-2070) for three Representative Concentration Pathway (RCP) scenarios, RCP 2.6, 4.5, and 8.5 using the Canadian Earth System Model Second Generation (CanESM2). The results revealed a monotonic rise in the HI and extreme caution conditions, especially in the humid summer season for most parts of Bangladesh for the observed period (1985-2015). Future projections revealed a continuous rise in HI in the forthcoming period (2041-2070). A higher and remarkable increase in the HI was projected in the northern, northeastern, and south-central regions. Among the three scenarios, the RCP 8.5 showed a higher projection of HI both in hot and humid summer compared to the other scenarios. Therefore, Bangladesh should take region-specific adaptation strategies to mitigate the impacts of HI.Supplementary Information: The online version contains supplementary material available at 10.1007/s00704-021-03705-x.