The Canary Islands hotspot consists of seven volcanic islands, mainly of Neogene age, rooted on oceanic Jurassic lithosphere. Its complex structure and geodynamic setting have led to different hypotheses about its origin and evolution, which is still a matter of a vivid debate. In addition to the classic mantle plume hypothesis, a mechanism of small-scale mantle convection at the edge of cratons (Edge Driven Convection, EDC) has been proposed due to the close proximity of the archipelago to the NW edge of the NW African Craton. A combination of mantle plume upwelling and EDC has also been hypothesized. In this study we evaluate these hypotheses quantitatively by means of numerical two-dimensional thermo-mechanical models. We find that models assuming only EDC require sharp edges of the craton and predict too narrow areas of partial melting. Models where the ascent of an upper-mantle plume is forced result in an asymmetric mantle flow pattern due to the interplay between the plume and the strongly heterogeneous lithosphere. The resulting thermal anomaly in the asthenosphere migrates laterally, in agreement with the overall westward decrease of the age of the islands. We suggest that laterally moving plumes related to strong lithospheric heterogeneities could explain the observed discrepancies between geochronologically estimated hotspot rates and plate velocities for many hotspots.