Pb-stearate multilayers prepared by the Langmuir-Blodgett (LB) technique on silicon show a change of layer structure just below the melting point. At temperatures between 98 degrees C and 112 degrees C the samples have been investigated by energy dispersive X-ray scattering in specular and diffuse scattering geometry. The time constants of the transition at fixed temperature was determined. After the disappearance of the old structure, new Bragg peaks grow out of an amorphous intermediate phase corresponding to a 20% smaller layer distance compared with the initial LB structure. At fixed temperature the intensity of the respective Bragg peaks increases and, after reaching a maximum, it decreases again until the new peaks disappear. Maximum Bragg intensity was observed at a transition temperature of 106 degrees C. The new phase is instable in time. Our results are compared with related effects of Cd stearate, which have been interpreted as a transformation into a two-dimensional ordered hexagonal structure of long columns.