We present a two-dimensional lithospheric thermal and density model along a transect running from the southwestern Iberian Peninsula to the northwestern Sahara. The main goal is to investigate the lithosphere structure underneath the Gulf of Cadiz and the Atlas Mountains. The model is based on the assumption of topography in local isostatic equilibrium and is constrained by surface heat flow, gravity anomalies, geoid, and topography data. The crustal structure has been constrained by seismic and geological data where available. Mantle density is supposed to vary linearly with temperature, providing the link between thermal and density-related data. The lithospheric thickness varies strongly along the profile, going from near 100 km under the Iberian Peninsula to at least 160--190 km under the Gulf of Cadiz and the Gharb foreland basin in Morocco and to 70 km underneath the Atlas Mountains, coinciding with a region of Neogene volcanism. The thickening of the lithosphere is interpreted as a SW trending lithospheric slab extending from the western Betics to the Gulf of Cadiz and the Gharb Basin, whereas the thin lithosphere underneath the Atlas may be interpreted as plume-like asthenospheric upwelling similar to those observed in the west European Alpine foreland or as a side effect of a slab penetrating the less viscous asthenosphere.