A step in the depth of the lithosphere base, associated with lateral variations in the upper mantle temperature structure, can trigger mantle flow that is referred to as edge-driven convection. This paper aims at outlining the implications of such edge-driven flow at a lateral temperature transition from a hot and thin to a cold and thick lithosphere of a continental back-arc. This configuration finds application in the southern Canadian Cordillera, where a hot and thin back-arc is adjacent to the cold and thick North American Craton. A series of geodynamical models tested the thermodynamical behavior of the lithosphere and upper mantle induced by a step in lithosphere thickness. The mantle flow patterns, thickness and heat flow evolution of the lithosphere, and surface topography are examined. We find that the lateral temperature transition shifts cratonward due to the vigorous edge-driven mantle flow that erodes the craton edge, unless the craton has a distinct high viscosity mantle lithosphere. The mantle lithosphere viscosity structure determines the impact of edge-driven flow on crustal deformation and surface heat flow; a dry olivine rheology for the craton prevents the edge from migrating and supports a persistent surface heat flow contrast. These phenomena are well illustrated at the transition from the hot Canadian Cordillera to craton that is supported by a rheological change and that coincides with a lateral change in surface heat flow. Fast seismic wave velocities observed in the upper mantle cratonward of the step can be explained as downwellings induced by the edge-driven flow.