  We investigate the thermodynamics of spherically symmetric black hole
solutions in a four-dimensional Einstein--Yang-Mills-SU(2) theory with a
negative cosmological constant. Special attention is paid to configurations
with a unit magnetic charge. We find that a set of
Reissner-Nordstr\"om--Anti-de Sitter black holes can become unstable to forming
non-Abelian hair. However, the hairy black holes are never thermodynamically
favoured over the full set of abelian monopole solutions. The thermodynamics of
the generic configurations possessing a noninteger magnetic charge is also
discussed.
