The temporal evolution of sea ice salinity affects the temperature profile and vertical growth and decay of the ice cover, as well as many other important properties. Here, we use a one-dimensional thermodynamic sea ice model to explore the sensitivity to the vertical profile of ice salinity of (1) Arctic first-year and equilibrium multiyear sea ice thickness, and (2) the salt/freshwater flux at the ice/ocean interface. Results indicate that increasing the mean salinity induces a higher thermal inertia reducing summer melt and finally increasing ice thickness. The shape of the profile is also important, since low salinity at the surface must be captured to produce enough surface melt. This study gives accurate hints on what the minimum complexity of a parameterization of the temporal evolution of sea ice salinity should be.