  The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three
dimensional spinless $p_x+ip_y$ superconductor provide an intriguing example of
a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of
the Altland-Zirnbauer symmetry classification; such a phase can support a large
anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs
at zero energy. We study the effect of quenched disorder on such a topological
phase with both numerical and analytical methods. Using the kernel polynomial
method, we compute the average and typical density of states for the BdG
quasiparticles; based on this, we construct the disordered phase diagram. We
show for infinitesimal disorder, the ThSM is converted into a diffusive thermal
Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase
diagram of the disordered model only consists of ThDM and thermal insulating
phases. Nonetheless, there is a cross-over at finite energies from a ThSM
regime to a ThDM regime, and we establish the scaling properties of the avoided
quantum critical point which marks this cross-over. Additionally, we show the
existence of two types of thermal insulators: (i) a trivial thermal band
insulator (ThBI) [or BEC phase] supporting only exponentially localized
Lifshitz states (at low energy), and (ii) a thermal Anderson insulator (AI) at
large disorder strengths. We determine the nature of the two distinct
localization transitions between these two types of insulators and ThDM.We also
discuss the experimental relevance of our results for three dimensional, time
reversal symmetry breaking, triplet superconducting states.
