  We study the influence of the rattling phonons on superconductivity in
$\beta$-pyrochlore KOs$_{2}$O$_{6}$ compound based on the strong-coupling
Eliashberg approach. In particular, analyzing the specific heat data we find
that the rattling phonon frequency changes discontinuously at the critical
temperature of the first order phase transition. Solving the strong-coupling
Eliashberg equations with temperature dependent $\alpha^{2}F(\omega)$, we
investigate the consequence of this first order phase transition for the
anomalous temperature dependence of the superconducting gap. We discuss our
results in context of the recent experimental data.
