  Proposed effective Hamiltonians from the literature for the material
$\alpha$-RuCl${}_3$ are used to compute the magnon thermal Hall conductivity,
$\kappa_{xy}$, using linear spin wave theory for the magnetically ordered
state. No model previously proposed that was tested explains published
experimental data. Models with Kitaev interaction $K>0$ are seen to predict
$\kappa_{xy}\gtrsim 0$, which is inconsistent with the data. Fluctuations
toward a Kitaev-type spin liquid would have the wrong sign to explain the data.
However, a slight variant of a previously proposed model predicts a large
$\kappa_{xy}$, demonstrating that the low-temperature thermal Hall effect could
be generated exclusively by the Berry curvature of the magnon bands. The
experimental data of $\kappa_{xy}$ can therefore serve as another method to
constrain a proposed effective Hamiltonian.
