  We study the thermoelectric properties of a double-Weyl fermion system,
possibly realized in $\mathrm{HgCr_2Se_4}$ and $\mathrm{SrSi_2}$, by a
semi-classical Boltzmann transport theory. We investigate different relaxation
processes including short-range disorder and electron-electron interaction on
the thermoelectric transport coefficients. It is found that the anisotropy of
the band dispersion for in-plane and out-of-plane momentum directions affects
the relaxation time for transport in different directions. The transport also
exhibits an interesting directional dependence on the chemical potential and
model parameters, differing from a simple isotropic quadratic or linearly
dispersing electron gas. By applying a static magnetic field along the linearly
dispersing direction, the longitudinal and transverse electrical and thermal
magnetoconductivity show a similar dependence on the in-plane cyclotron
frequency to the linear dispersing Weyl nodes. By including internode
scattering, we find that the chiral anomaly contribution to the thermoelectric
coefficients doubles that of a linearly dispersing Weyl node in both the
semi-classical and quantum regimes. A magnetic field applied along the
quadratically dispersing direction will split the double Weyl point into two
single Weyl points with the same chirality.
