Both climate change and rapid urbanization accelerate exposure to heat in the city of Kampala, Uganda. From a network of low-cost temperature and humidity sensors, operational in 2018-2019, we derive the daily mean, minimum and maximum Humidex in order to quantify and explain intra-urban heat stress variation. This temperature-humidity index is shown to be heterogeneously distributed over the city, with a daily mean intra-urban Humidex Index deviation of 1.2 degrees C on average. The largest difference between the coolest and the warmest station occurs between 16:00 and 17:00 local time. Averaged over the whole observation period, this daily maximum difference is 6.4 degrees C between the warmest and coolest stations, and reaches 14.5 degrees C on the most extreme day. This heat stress heterogeneity also translates to the occurrence of extreme heat, shown in other parts of the world to put local populations at risk of great discomfort or health danger. One station in a dense settlement reports a daily maximum Humidex Index of >40 degrees C in 68% of the observation days, a level which was never reached at the nearby campus of the Makerere University, and only a few times at the city outskirts. Large intra-urban heat stress differences are explained by satellite earth observation products. Normalized Difference Vegetation Index has the highest (75%) power to predict the intra-urban variations in daily mean heat stress, but strong collinearity is found with other variables like impervious surface fraction and population density. Our results have implications for urban planning on the one hand, highlighting the importance of urban greening, and risk management on the other hand, recommending the use of a temperature-humidity index and accounting for large intra-urban heat stress variations and heat-prone districts in urban heat action plans for tropical humid cities.