Desert dust aerosols are the most prominent tropospheric aerosols, playing an important role in the earth's climate. However, their radiative forcing is currently not known with sufficient precision to even determine its sign. The sources of uncertainty are multiple, one of them being a poor characterisation of the dust aerosol's vertical profile on a global scale. In this work, we tackle this scientific issue by designing a method for retrieving dust aerosol vertical profiles from Thermal Infrared measurements by Infrared Atmospheric Sounding Interferometer (IASI) instruments onboard the Metop satellite series. IASI offers almost global coverage twice a day, and long (past and future) time series of radiances, therefore being extremely well suited for climate studies. Our retrieval follows Rodger's formalism and is based on a two-step approach, treating separately the issues of low altitude sensitivity and difficult a priori definition. We compare our results for a selected test case above the Atlantic Ocean and North Africa in June 2009, with optical depth data from MODIS, aerosol absorbing index from GOME-2 and OMI, and vertical profiles of extinction coefficients from CALIOP. We also use literature information on desert dust sources to interpret our results above land. Our retrievals provide perfectly reasonable results in terms of optical depth. The retrieved vertical profiles (with on average 1.5 degrees of freedom) show most of the time sensitivity down to the lowest layer, and agree well with CALIOP extinction profiles for medium to high dust optical depth. We conclude that this new method is extremely promising for improving the scientific knowledge about the 3-D distribution of desert dust aerosols in the atmosphere.