  It was recently pointed out by Barrau, Martineau and Renevey that the mass of
the Schwarzschild black hole immersed in a heat bath tends to infity in a
finite time. We show that this singularity problem in the black hole mass may
be avoided, if the stretched horizon of the black hole is constructed out of a
fixed, finite number of discrete constituents, and an appropriate counting is
applied to the energy eigenstates of the hole.
