Extreme weather events are major causes of loss of life and damage infrastructure worldwide. High temperatures cause heat stress on humans, livestock, crops and infrastructure. Heat stress exposure is projected to increase with ongoing climate change. Extremes of temperature are common in Africa and infrastructure is often incapable of providing adequate cooling. We show how easily accessible cooling technology, such as evaporative coolers, prevent heat stress in historic timescales but are unsuitable as a solution under climate change. As temperatures increase, powered cooling, such as air conditioning, is necessary to prevent overheating. This will, in turn, increase demand on already stretched infrastructure. We use high temporal resolution climate model data to estimate the demand for cooling according to two metrics, firstly the apparent temperature and secondly the discomfort index. For each grid cell we calculate the heat stress value and the amount of cooling required to turn a heat stress event into a non heat stress event. We show the increase in demand for cooling in Africa is non uniform and that equatorial countries are exposed to higher heat stress than higher latitude countries. We further show that evaporative coolers are less effective in tropical regions than in the extra tropics. Finally, we show that neither low nor high efficiency coolers are sufficient to return Africa to current levels of heat stress under climate change.