  We study, within a framework of the classical fields approximation, the
static structure factor of a weakly interacting Bose gas at thermal
equilibrium. As in a recent experiment (R. Schley et al., Phys. Rev. Lett. 111,
055301 (2013)), we find that the thermal distribution of phonons in a
three-dimensional Bose gas follows the Planck distribution. On the other hand
we find a disagreement between the Planck and phonon (calculated just like for
the bulk gas) distributions in the case of elongated quasi-one-dimensional
systems. We attribute this discrepancy to the existence of spontaneous dark
solitons (i.e., thermal solitons as reported in T. Karpiuk et al., Phys. Rev.
Lett. 109, 205302 (2012)) in an elongated Bose gas at thermal equilibrium.
