  We investigate the phase diagram of a three-dimensional, time-reversal
symmetric topological superconductor in the presence of charge impurities and
random $s$-wave pairing. Combining complimentary field theoretic and numerical
methods, we show that the quantum phase transition between two topologically
distinct paired states (or thermal insulators), described by thermal Dirac
semimetal, remains unaffected in the presence of sufficiently weak generic
randomness. At stronger disorder, however, these two phases are separated by an
intervening thermal metallic phase of diffusive Majorana fermions. We show that
across the insulator-insulator and metal-insulator transitions, normalized
thermal conductance displays single parameter scaling, allowing us to
numerically extract the critical exponents across them. The pertinence of our
study in strong spin-orbit coupled, three-dimensional doped narrow gap
semiconductors, such as Cu$_x$Bi$_2$Se$_3$, is discussed.
