We have performed a detailed ex situ magneto-optical investigation into the magnetic properties of wedged ultrathin epitaxial Ag/Fe/Ag(001) films as a function of both temperature and Fe thickness. The Fe thickness dependent reorientation phase transition (RPT) of the magnetic easy direction from out-of-plane to in-plane has been studied at various temperatures in the range 2-180 K. By using the polar Kerr effect and the Cotton-Mouton effect in reflection we were able to probe simultaneously the out-of-plane and in-plane magnetization components. We report the thermally activated formation of an out-of-plane domain structure at remanence: at low temperatures the structure can only nucleate for small perpendicular anisotropy, i.e., close to the RPT Fe thickness; at higher temperatures nucleation is possible for Fe thicknesses well below the RPT thickness. We also report that the bulk cubic anisotropy term, K-1, changes sign in the vicinity of the RPT Fe thickness. Consequently, we are able to delineate an Fe thickness-temperature Phase diagram which identifies at least one point in (Fe thickness, temperature) space where the RPT coincides with vanishing K-1. The identification of such a point is a necessary step towards the realization of a two-dimensional Heisenberg magnet.