This study examines mutual interactions between stationary waves and ice sheets using a dry atmospheric primitive-equation model coupled to a three-dimensional thermomechanical ice-sheet model. The emphasis is on how nonlinear interactions between thermal and topographical forcing of the stationary waves influence the ice-sheet evolution through the ablation. Simulations are conducted in which a small ice cap, on an idealised Northern Hemisphere continent, evolves to an equilibrium continental-scale ice sheet. In the absence of stationary waves, the equilibrium ice sheet arrives at symmetric shape with a zonal equatorward margin. In isolation, the topographically-induced stationary waves have essentially no impacton the equilibrium features of the ice sheet. The reason is that the response is nonlinearimplying that the temperature anomalies are located far from the equatorward ice margin. When forcing due to thermal cooling is added to the topographical forcing, thermally-induced perturbation winds amplify the topographically-induced stationary-wave response, which serves to increase the equatorward extent of the ice sheet. Hence, the present study suggests that, if the topographically-induced stationary-wave response is nonlinear, it can be substantially amplified by the high albedo of the ice-sheet surface.