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The Sahel region of West Africa experiences decadal swings between periods of drought and abundant rainfall, and a large body of work asserts that these variations in the West African monsoon are a response to changes in the temperatures of the tropical Atlantic and Indian Oceans. However, here it is shown that when forced by SST alone, most state-of-the-art climate models do not reproduce a statistically significant upward trend in Sahelian precipitation over the last 30 years and that those models with a significant upward trend in rainfall seem to achieve this result for disparate reasons. Here the role of the Saharan heat low (SHL) in the recovery from the Sahelian drought of the 1980s is examined. Using observations and reanalyses, it is demonstrated that there has been an upward trend in SHL temperature that is coincident with the drought recovery. A heat and moisture budget analysis of the SHL suggests that the rise in temperature is due to greenhouse warming by water vapor, but that changes in water vapor are strongly dependent upon the temperature of the SHL: a process termed the Saharan water vapor-temperature (SWAT) feedback. It is shown that the structure of the drought recovery is consistent with a warming SHL and is evidence of a fundamental, but not exclusive, role for the SHL in the recent increase in Sahelian monsoon rainfall.