  We report a study of thermal conductivity and resistivity at ultra-low
temperatures and in high magnetic fields for semi-metal materials TaAs$_2$ and
NbAs$_2$ by using single crystal samples. The thermal conductivity is strongly
suppressed in magnetic fields, having good correspondence with the large
positive magnetoresistance, which indicates a dominant electronic contribution
to thermal conductivity. In addition, not only the resistivity but also the
thermal conductivity display clear quantum oscillations behavior at subKelvin
temperatures and in magnetic fields up to 14 T. The most striking phenomenon is
that the thermal conductivity show a $T^4$ behavior at very low temperatures,
while the resistivity show a $T$-independent behavior. This indicates a strong
violation of the Weidemann-Franz law and points to a non-Feimi liquid state of
these materials.
