Plate reconstructions show that the plume feeding today’s Icelandic volcanism passed beneath the continental lithosphere of Greenland between 50 and 100 million years ago. While there has been ample volcanism on the margins of Greenland, both on the west and the east coasts, the thickness of the Greenland craton prevented surface eruptions within Greenland, leaving details of the plume track unclear. However, the passage of the plume is expected to leave a scar in the lower continental lithosphere of Greenland, where the hot plume material interacts with and erodes the stiff cratonic root. This interaction should cause increased surface heat flux and reduced lithosphere thickness along the plume track, and can potentially be constrained by observations that constrain heat flux (e.g., magnetic data and ice flow rates) and lithospheric structure (e.g., seismic tomography and magnetotelluric modeling). While most seismic tomography models indicate that there might be an east-west trending corridor of reduced lithosphere thickness, recent heat flux maps inferred from magnetic data show a northwest-southeast trending anomaly of high heat flux, suggesting an alternative direction of the passage of the Iceland plume. In order to resolve the discrepancy between the suggested hotspot tracks, we use numerical models to investigate how the surface heat flux would evolve in response to the passage of a plume beneath thick cratonic lithosphere. Our work focuses both on the temporal evolution (e.g. the onset and duration), and the shape of the heat flux anomaly, as well as lithospheric thinning related to convective erosion of the cratonic root by hot plume material. We show that both the onset and the duration of the heat flux anomaly, as well as the degree of lithosphere thinning, depend on various parameters, especially the viscosity structure of lithosphere and asthenosphere and the plume strength. A comparison between observations from Greenland and our model predictions should provide new and better constraints on the subsurface structure of Greenland, and how it was modified by its interaction with the Iceland plume.