X-ray reflectivity measurements of the free surface of a C(12)E(5) + water mixture at a mass fraction of the surfactant of 0.4 are presented. This system forms a hexagonal LC-phase at ambient temperatures. At a temperature of T = 23.82 degrees C the typical Bragg pattern for hexagonal symmetry is no longer observed when the angle of incidence of the beam is larger than the critical angle of total external reflection, alpha(c). If the angle of incidence is smaller than alpha(c), well-pronounced reflexes are observed at the same temperature. This shows that the anisotropic phase is stable to higher temperatures at the surface as compared to the bulk.