  We report a heat switch effect in single crystals of an antiferromagnet
Co$_3$V$_2$O$_8$, that is, the thermal conductivity ($\kappa$) can be changed
with magnetic field in an extremely large scale. Due to successive magnetic
phase transitions at 12--6 K, the zero-field $\kappa(T)$ displays a deep
minimum at 6.7 K and rather small magnitude at low temperatures. Both the
temperature and field dependencies of $\kappa$ demonstrate that the phonons are
strongly scattered at the regime of magnetic phase transitions. Magnetic field
can suppress magnetic scattering effect and significantly recover the phonon
thermal conductivity. In particular, a 14 T field along the $a$ axis increases
the $\kappa$ at 7.5 K up to 100 times. For $H \parallel c$, the magnitude of
$\kappa$ can be suppressed down to $\sim$ 8% at some field-induced transition
and can be enhanced up to 20 times at 14 T. The present results demonstrate
that it is possible to design a kind of heat switch in the family of magnetic
materials.
