Summary: Using the Euclidean action with constraints eliminated, we investigate the thermodynamics of the spherical black hole-global monopole system. It is shown that there indeed exists a stable thermal equilibrium for the system in the canonical ensemble in which the temperature and surface area are fixed at a finite boundary. A comparison with ordinary black holes under equivalent boundary conditions indicates that if such a system exists, it will not decay spontaneously to a black hole without a global monopole. See also H. Yu, Euclidean action partition function and thermodynamics of a block-hole global-monopole system, Classical Gravity 12, No. 12, 3077-3083 (1995; Zbl 0838.53069).