Abstract In this study, the response of sea ice thickness to changes in the external forcing is investigated and particularly how this response depends on the surface albedo formulation by means of a one-dimensional coupled ocean–ice–atmosphere model. The main focus is on the thickness response to the atmospheric heat advection Fwall, solar radiation FSW, and amount of snow precipitation Sprec. Different albedo parameterization schemes [ECHAM5, CSIRO, and Community Climate System Model, version 3 (CCSM3)] representing albedos commonly used in global climate models are compared together with more simplified schemes. Using different albedo schemes with the same external forcing produces large differences in ice thickness. The ice thickness response is similar for all realistic albedo schemes with a nearly linear decrease with increasing Fwall in the perennial ice regime and with a steplike transition into seasonal ice when Fwall exceeds a certain threshold. This transition occurs at an annual-mean ice thickness of 1.7–2.0 m. Latitudinal differences in solar insolation generally leads to increasing ice thickness toward the North Pole. The snow response varies significantly depending on which albedo scheme is used. The ECHAM5 scheme yields thinner ice with Sprec, the CSIRO scheme gives ice thickness nearly independent of Sprec, and with the CCSM3 scheme the ice thickness decreases with Sprec. A general result is that the modeled ice cover is rather sensitive to positive perturbations of the external heat supply when it is close to the transition such that just a small increase of, for example, Fwall can force the ice cover into the seasonal regime.