  We present measurements of the thermal conductivity $\kappa $ and the thermal
expansion $\alpha$ of NdMnO$_3$ and TbMnO$_3$. In both compounds a splitting of
the $4f$ multiplet of the $R^{3+}$ ion causes Schottky contributions to
$\alpha$. In TbMnO$_3$ this contribution arises from a crystal-field splitting,
while in NdMnO$_3$ it is due to the Nd-Mn exchange coupling. Another
consequence of this coupling is a strongly enhanced canting of the Mn moments.
The thermal conductivity is greatly suppressed in both compounds. The main
scattering process at low temperatures is resonant scattering of phonons
between different energy levels of the $4f$ multiplets, whereas the complex 3d
magnetism of the Mn ions is of minor importance.
