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The West African Monsoon (WAM) and its representation in numerical models is heavily influenced by the Saharan heat low (SHL), a low-pressure system driven by radiative heating over the central Sahara and ventilated by the cold and moist inflow from adjacent oceans. It has recently been shown that a significant part of the southerly moisture flux into the SHL originates from convective cold pools over the Sahel. These density currents driven by evaporation of rain are largely missing in models with parameterized convection. This crucial issue has been hypothesized to contribute to the inability of many climate models to reproduce the variability of the WAM. Observations from the Atlas Mountains, located at the northern flank of the SHL, indicate frequent convection and cold-pool generation during boreal summer, often during episodes of multiple days. This study is the first to analyze impacts of such convective periods on the SHL, based on simulations of two example cases using the Weather Research and Forecast (WRF) model at convection-permitting resolution. Sensitivity experiments with artificially removed cold pools, lower resolutions, and parameterizations are conducted. Results indicate that cold pools lead to increases in surface pressure of more than 1 hPa and significant moisture transports into the desert over several days. This moisture affects radiative heating and thus the energy balance of the SHL. Together with studies focusing on the Sahel, this work emphasizes the need for improved parameterization schemes for deep convection in order to produce more reliable climate projections for the WAM.