  We investigate the anomalous thermal Hall effect (ATHE) in Weyl
superconductors realized by the $E_{1u}$ ($p$-wave and $f$-wave) chiral
superconducting order for the point group $D_{6h}$. Using the quasiclassical
Eilenberger theory, we analyze the influence of the impurity scattering and the
line nodal excitations on the ATHE, and compare it with the intrinsic
(topological) contribution. Because the transverse response is sensitive to the
slope of the density of states at the Fermi surface, the extrinsic ATHE
vanishes in both the weak (Born) and strong (unitarity) scattering limits. The
thermal Hall conductivity (THC) is maximal at intermediate impurity strengths
when there is a large slope of the density states in the impurity bands close
to the Fermi energy. Under these conditions, the extrinsic ATHE dominates the
intrinsic ATHE even at low temperatures. The extrinsic ATHE is sensitive to
line nodal excitations, whereas the intrinsic ATHE is not. When the line nodes
in the gap involve the sign change of the order parameter, the extrinsic
contribution to the THC is suppressed even though the phase space for low
energy excitation is large. In contrast, if the nodes are not accompanied by
such a sign change, the extrinsic ATHE is significantly enhanced. Our results
form a basis for the comprehensive analysis of anomalous thermal transport in
Weyl superconductors.
