Combined small-angle neutron and X-ray scattering experiments on dilute solutions of the ganglioside GM3 in water are presented. The contrast profiles along the lipid and sugar portions of the ganglioside molecule for the two types of radiations are different, a feature which, added to the extension of the scattering q range to q similar to 0.4 Angstrom(-1), allows an accurate determination of the cross section of the bilayer in dilute solution. The electronic density profile of the bilayer cross section can be interpreted only by assuming thickness fluctuations, which have already been theoretically predicted for the GM3 bilayers, due to the peculiar packing properties of the monomer. Increasing temperature from room temperature to 50 degrees C has the effect of flattening the GM3 bilayer, as the thickness and the water content of the outer hydrophilic layer decrease, while the thickness of the inner hydrophobic region is almost unchanged.