  We report on the phonon spectrum probed at the $\beta$--FeSe(001) surface by
means of high-resolution electron energy-loss spectroscopy (HREELS). Single
crystals of $\beta$--FeSe are cleaved under ultra-high vacuum conditions and
are subsequently measured below and above the nematic transition temperature.
In total we observe five phonon modes and a phonon cutoff energy of about 40
meV. We identify the origin of each phonon mode based on the selection rules of
HREELS and by comparing the experimental results to the ones of \emph{ab
initio} density functional calculations. The most prominent phonon modes
$A_{1g}$, $B_{1g}$, and $A_{2u}$ appear at energies of about $20.5$ and $25.6$
and $40$ meV, respectively. These phonon modes disperse rather weakly while
changing the momentum from zero up to the zone boundary, indicating that they
are mainly of optical nature. A comparison between our results and the results
of \emph{ab initio} calculations indicates that there must be a mutual
interplay between magnetism and lattice dynamics in this compound, similar to
the other Fe-based superconductors. Finally, we comment on the role of
temperature on the phonon modes probed at the $\bar{\Gamma}$--point. It is
observed that both the $B_{1g}$ and $A_{2u}$ phonon modes undergo a downward
shift while increasing the temperature from 15 to 300 K. In the case of the
$A_{2u}$ mode this shift is about 1.5 meV.
