Ultrathin ferromagnetic films have been found to exhibit a strongly enhanced magnetocrystalline anisotropy, which can even be sufficient to overcome the demagnetizing effect and stabilize a perpendicular magnetized state in the entire ferromagnetic temperature range. Such perpendicular magnetized systems have been particularly interesting with respect their thermodynamic properties and were reported to confirm predictions for the two-dimensional Ising model. However, recent experiments on perpendicular magnetized Ni/Cu(100)-films have shown indications for domain formation near the Curie temperature that seems to occur without weakening of the effective anisotropy (crystalline + dipolar).@footnote 1@ Therefore, this observation seems to be fundamentally different from earlier results reported for a number of ultrathin film systems where domain formation is found in the immediate vicinity of the reorientation phase transition, which is associated with the vanishing of the effective anisotropy. To understand the above phenomena we have evaluated the free energy of a perpendicular magnetized material using the Ginzburg-Landau theory. In accordance with previous results, we find that for sufficiently large anisotropy values no conventional domain structure is formed at any temperature. However, we find that a domain structure based on the formation of linear domain walls (LDW-phase) lowers the energy in a substantial region around the critical point. In addition, the domain size is estimated to be microscopically small so that this domain structure should be formed for any realistic sample size. We will discuss the details of the calculated phase diagram with particular emphasis on the implication that the LDW-phase prohibits a direct ferromagnetic, paramagnetic phase transition. Work supported by the U. S. Department of Energy, Basic Energy Sciences, Materials Science under Contract W-31-109-ENG-38. @FootnoteText@ @footnote 1@P. Poulopoulos et al., Phys. Rev. B 55, 11961 (1997).