  We investigate the thermodynamics of a general class of exact 4-dimensional
asymptotically Anti-de Sitter hairy black hole solutions and show that, for a
fixed temperature, there are small and large hairy black holes similar to the
Schwarzschild-AdS black hole. The large black holes have positive specific heat
and so they can be in equilibrium with a thermal bath of radiation at the
Hawking temperature. The relevant thermodynamic quantities are computed by
using the Hamiltonian formalism and counterterm method. We explicitly show that
there are first order phase transitions similar to the Hawking-Page phase
transition.
