  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.
