  We demonstrate that the reorientation transition from out-of-plane to
in-plane magnetization with decreasing temperature as observed experimentally
in Ni-films on Cu(001) can be explained on a microscopic basis. Using a
combination of mean field theory and perturbation theory, we derive an analytic
expression for the temperature dependent anisotropy. The reduced magnetization
in the film surface at finite temperatures plays a crucial role for this
transition as with increasing temperature the influence of the uniaxial
anisotropies is reduced at the surface and is enhanced inside the film.
