  The observed Lyman-$\alpha$ flux power spectrum (FPS) is suppressed on scales
below $\sim~ 30~{\rm km~s}^{-1}$. This cutoff could be due to the high
temperature, $T_0$, and pressure, $p_0$, of the absorbing gas or,
alternatively, it could reflect the free streaming of dark matter particles in
the early universe. We perform a set of very high resolution cosmological
hydrodynamic simulations in which we vary $T_0$, $p_0$ and the amplitude of the
dark matter free streaming, and compare the FPS of mock spectra to the data. We
show that the location of the dark matter free-streaming cutoff scales
differently with redshift than the cutoff produced by thermal effects and is
more pronounced at higher redshift. We, therefore, focus on a comparison to the
observed FPS at $z>5$. We demonstrate that the FPS cutoff can be fit assuming
cold dark matter, but it can be equally well fit assuming that the dark matter
consists of $\sim 7$ keV sterile neutrinos in which case the cutoff is due
primarily to the dark matter free streaming.
