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Global warming and extreme heat events have well-documented adverse effects on human health. As a first step to understand the possible future risk for heat-related illness and mortality, this study analyzes climate model projections to constrain model variability and spread related to humid heat extremes over Africa. Using CMIP6, CESM2-LE, CORDEX and CMIP5 models, we examine the impacts of model uncertainty, horizontal resolution, and internal variability on projections of heat indices, including wet bulb temperature, wet bulb globe temperature, Humidex, and the Extended Heat Index, over the next century. Across resolutions and model types, humid heat projections under moderate greenhouse gas emission scenarios (SSP245/RCP45) indicate that Sub-Saharan Africa will experience a higher count of extreme heat events over the next century compared to the rest of the continent. Within CESM2-LE, the trends in humid heat metrics are driven almost entirely by external forcings (i.e., increasing greenhouse gas emissions), except in parts of Central, Northeast, and Southeast Africa, where natural variability accounts for roughly 10-18\% of the total variance. Model resolution has a significant impact on the simulated number of extreme humid heat events; low-resolution models from CMIP5 project roughly 40-80 more extreme event days per year over Central Africa by the end of the century compared to their corresponding downscaled CORDEX models. This work serves as a key precursor to future studies projecting heat-health outcomes due to climate change over Africa.