  In frustrated magnets the Dzyaloshinsky-Moriya interaction arising from
spin-orbit coupling can induce a magnetic long-range order. Here, we report a
theoretical prediction of thermal Hall effect in frustrated kagom\'e magnets
such as KCr$_3$(OH)$_6$(SO4)$_2$ and KFe$_3$(OH)$_{6}$(SO$_{4}$)$_2$. The
thermal Hall effects in these materials are induced by scalar spin chirality as
opposed to DMI in previous studies. The scalar spin chirality originates from
magnetic-field-induced chiral spin configuration due to non-coplanar spin
textures, but in general it can be spontaneously developed as a macroscopic
order parameter in chiral quantum spin liquids. Therefore, we infer that there
is a possibility of thermal Hall effect in frustrated kagom\'e magnets such as
herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$ and the chromium compound
Ca$_{10}$Cr$_7$O$_{28}$, although they also show evidence of magnetic order in
the presence of a magnetic field or pressure.
