We report the results of grazing incidence X-ray diffraction studies, as a function of temperature, of monolayers of perfluoro-n-eicosane. The experiments were undertaken to test the suggestion that there is a phase transition in this monolayer between 20 and 25 degrees C, in analogy with the transition which occurs in Teflon at about the same temperature. The issue is of importance with respect to determining whether description of the properties of a monolayer requires consideration of only the obvious quasi two dimensional character of the monolayer or requires inclusion of its three dimensional character. Our results do not support the existence of the suggested transition.