  Th$_3$Te$_4$ materials are potential candidates for commercial thermoelectric
(TE) materials at high-temperature due to their superior physical properties.
We incorporate the multiband Boltzmann transport equations with firstprinciples
calculations to theoretically investigate the TE properties of Th$_3$Te$_4$
materials. As a demonstration of our method, the TE properties of La$_3$Te$_4$
are similar with that of Ce$_3$Te$_4$ at low-temperature, which is consistent
with the experiment. Then we systematically calculate the electrical
conductivity, the Seebeck coefficient, and the power factor of the two
materials above based on parameters obtained from first-principles calculations
as well as several other fitting parameters. Our results reveal that for the
electron--optical-phonon scattering at high temperatures, a linear dependence
of optical phonon energy on temperature explains better the experimental
results than a constant optical phonon energy. Based on this, we predict that
the TE properties of Ce$_3$Te$_4$ is better than La$_3$Te$_4$ at high
temperatures and the optimal carrier concentration corresponding to
Ce$_3$Te$_4$ shifts upward with increasing temperature. The optimal carrier
concentration of Ce$_3$Te$_4$ is around $1.6\times10^{21}$cm$^{-3}$ with the
peak power factor 13.07 $\mu$Wcm$^{-1}$K$^{-2}$ at $T=1200$K.
