We present a two-dimensional, coupled, mesoscale atmosphere–sea-ice model, and apply it to simulate the air–ice interaction during warm-air advection. The model was run into a steady state under various conditions with respect to the season, cloud cover and wind speed. The spatial and temporal evolution of the thermodynamics of the ice, snow and the atmospheric boundary layer (ABL) were investigated. The development of the stably stratified ABL downwind of the ice edge depended above all on the wind speed and cloud cover. If the turbulent heat flux from air to snow was large enough to compensate the radiative cooling of the surface, a downward conductive heat flux was generated in the upper ice and snow layers. The stronger was the surface heating (strong wind, overcast skies) and the shorter its duration (on a scale down to a few hours), the wider was the region where this downward flux occurred. From the point of view of ABL modelling, the interactive coupling between air and ice was most important when the wind was strong, while from the point of view of ice thermodynamic modelling the coupling was most important when the wind was weak.