  In this paper, we have compared two different accretion mechanisms of dark
matter particles by a canonical neutron star with $M=1.4~M_{\odot}$ and
$R=10~{\rm km}$, and shown the effects of dark matter heating on the surface
temperature of star. We should take into account the Bondi accretion of dark
matter by neutron stars rather than the accretion mechanism of Kouvaris (2008)
\citep{Kouvaris08}, once the dark matter density is higher than $\sim3.81~\rm
GeV/cm^3$. Based on the Bondi accretion mechanism and heating of dark matter
annihilation, the surface temperature platform of star can appear at $\sim
10^{6.5}$ year and arrive $\sim 1.12\times10^5$ K for the dark matter density
of $3.81~\rm GeV/cm^3$, which is one order of magnitude higher than the case of
Kouvaris (2008) with dark matter density of $30~\rm GeV/cm^3$.
