We report on the analysis of FM selective reflection experiments on the 6S1/2->8P3/2 transition of Cs at 388 nm, and on the measurement of the surface van der Waals interaction exerted by a sapphire interface on Cs(8P3/2). Various improvements in the systematic fitting of the experiments have permitted to supersede the major difficulty of a severe overlap of the hyperfine components, originating on the one hand in a relatively small natural structure, and on the other hand on a large pressure broadening imposed by the high atomic density needed for the observation of selective reflection on a weak transition. The strength of the van der Waals surface interaction is evaluated to be 73$\pm$10 kHz.$\mu$m3. An evaluation of the pressure shift of the transition is also provided as a by-product of the measurement. We finally discuss the significance of an apparent disagreement between the experimental measurement of the surface interaction, and the theoretical value calculated for an electromagnetic vacuum at a null temperature. The possible influence of the thermal excitation of the surface is evoked, because, the dominant contributions to the vW interaction for Cs(8P3/2) lie in the far infrared range.