[en] We consider an fcc semi-infinite ferromagnetic insulator displaying an anisotropic exchange interaction between spins on the (111) surface plane of the form Jsub(parallel)[Ssub(i)sup(x)Ssub(j)sup(x)+Ssub(i)sup(y)Ssub(j)sup(y )+etaSsub(i)sup(z)Ssub(j)sup(z)], assuming all other interactions isotropic. A self-consistent RPA calculation is performed, with a Green function method valid for any spin S, up to the bulk transition temperature Tsub(c)sup(b), by imposing that the magnetization of the third layer equals the bulk value. For eta sufficiently large, the surface magnetization is non-zero for T>Tsub(c)sup(b), up to a transition temperature Tsub(c)sup(s)(eta) whenever eta>=etasub(c)>1, where Tsub(c)sup(s)(etasub(c))=Tsub(c)sup(b). For T>Tsub(c)sup(b) the system is equivalent to a film of three layers, where the magnetization of the third one is identically zero as a boundary condition. A discontinuity of the derivative in the curve of the magnetization of the first two layers vs. temperature is found at Tsub(c)sup(b). The results show clearly a cross-over from Heisenberg to Ising behaviour at the surface. (author)