The Arctic climate system is host to many processes which interact vertically over the tightly coupled atmosphere, sea ice and ocean. The coupled Atmosphere-Ocean Single-Column Model (AOSCM) allows to decouple local small-scale and large-scale processes to investigate the model performance in an idealized setting. Here, an observed Arctic warm air intrusion event is used to show how to identify model deficiencies using the AOSCM. The AOSCM allows us to effectively produce a large number of perturbation simulations, around 1,000, to map sensitivities of the model results due to changes in physical and model properties as well as to the large-scale tendencies. The analysis of the summary diagnostics, that is, aggregated results from sensitivity experiments evaluated against modeled physical properties, such as surface energy budget and mean sea ice thickness, reveals sensitivities to the chosen parameters. Further, we discuss how the conclusions can be used to understand the behavior of the global host model. The simulations confirm that the horizontal advection of heat and moisture plays an important role for maintaining a low-level cloud cover, as in earlier studies. The combined cloud layers increase the energy input to the surface, which in turn enhances the ongoing melt. The clouds present an additional sensitivity in terms of how they are represented but also their interaction with the large-scale advection and the model time step. The methodology can be used for a variety of other regions, where the coupling to the ocean is important.