  I use first principles calculations to investigate the thermal conductivity
of $\beta$-In$_2$O$_3$ and compare the results with that of
$\alpha$-Al$_2$O$_3$, $\beta$-Ga$_2$O$_3$, and KTaO$_3$. The calculated thermal
conductivity of $\beta$-In$_2$O$_3$ agrees well with the experimental data
obtain recently, which found that the low-temperature thermal conductivity in
this material can reach values above 1000 W/mK. I find that the calculated
thermal conductivity of $\beta$-Ga$_2$O$_3$ is larger than that of
$\beta$-In$_2$O$_3$ at all temperatures, which implies that $\beta$-Ga$_2$O$_3$
should also exhibit high values of thermal conductivity at low temperatures.
The thermal conductivity of KTaO$_3$ calculated ignoring the
temperature-dependent phonon softening of low-frequency modes give
high-temperature values similar that of $\beta$-Ga$_2$O$_3$. However, the
calculated thermal conductivity of KTaO$_3$ does not increase as steeply as
that of the binary compounds at low temperatures, which results in KTaO$_3$
having the lowest low-temperature thermal conductivity despite having acoustic
phonon velocities larger than that of $\beta$-Ga$_2$O$_3$ and
$\beta$-In$_2$O$_3$. I attribute this to the fact that the acoustic phonon
velocities at low frequencies in KTaO$_3$ is less uniformly distributed because
its acoustic phonon branches are more dispersive compared to the binary oxides,
which causes enhanced momentum loss even during the normal phonon-phonon
scattering processes. I also calculate thermal diffusivity using the
theoretically obtained thermal conductivity and heat capacity and find that all
four materials exhibit the expected $T^{-1}$ behavior at high temperatures.
Additionally, the calculated ratio of the average phonon scattering time to
Planckian time is larger than the lower bound of 1 that has been observed
empirically in numerous other materials.
