This paper studies the thermodynamical stability of regular BHs in AdS5
background. We investigate off-shell free energy of the system as a function of
temperature for different values of a "coupling constant" L=4 theta/l^2, where
the cosmological constant is Lambda = -3/l^2 and \sqrt{theta} is a "minimal
length". The parameter L admits a critical value, L_{inf}=0.2, corresponding to
the appearance of an inflexion point in the Hawking temperature. In the
weak-coupling regime L < L_{inf}, there are first order phase transitions at
different temperatures. Unlike the Hawking-Page case, at temperature 0\le T \le
T_{min} the ground state is populated by "cold" near-extremal BHs instead of a
pure radiation. On the other hand, for L \g L_{inf} only large,
thermodynamically stable, BHs exist.Comment: 12 pages; 6 Figures; accepted for publication in Int. J. Mod. Phys.
