  The monoclinic crystal structure of $\beta$-$\mathrm{Ga_2O_3}$ leads to
significant anisotropy of the thermal properties. The 2$\omega$-method is used
to measure the thermal diffusivity $D$ in [010] and [001] direction
respectively and to determine the thermal conductivity values $\lambda$ of the
[100], [010] and [001] direction from the same insulating Mg doped
$\beta$-$\mathrm{Ga_2O_3}$ single crystal. We detect a temperature independent
anisotropy factor of both the thermal diffusivity and conductivity values of
$D_{[010]}/D_{[001]}=\lambda_{[010]}/\lambda_{[001]}=1.4\pm 0.1$. The
temperature-dependence is in accord with phonon-phonon-Umklapp scattering
processes from 300 K down to 150 K. Below 150 K point-defect-scattering lowers
the estimated phonon-phonon-Umklapp-scattering values.
