  Materials able to rapidly switch between thermally conductive states by
external stimuli such as electric or magnetic fields can be used as
all-solid-state thermal switches and open a myriad of applications in heat
management, power generation and cooling. Here, we show that the large
magnetoresistance that occurs in the highly conducting semimetal
$\alpha$-WSi$_{2}$ single crystals leads to dramatically large changes in
thermal conductivity at temperatures <100 K. At temperatures <20 K, where
electron-phonon scattering is minimized, the thermal conductivity switching
ratio between zero field and a 9T applied field can be >7. We extract the
electronic and lattice components of the from the thermal conductivity
measurements and show that the Lorenz number for this material approximates the
theoretical value of L$_{0}$. From the heat capacity and thermal diffusivity,
the speed of thermal conductivity switching is estimated to range from 1 x
10$^{-4}$ seconds at 5 K to 0.2 seconds at 100 K for a 5-mm long sample. This
work shows that WSi$_{2}$, a highly conducting multi-carrier semimetal, is a
promising thermal switch component for low-temperature applications such
cyclical adiabatic demagnetization cooling, a technique that would enable
replacing $^{3}$He-based refrigerators.
