  Using the mass-smeared scheme of black holes, we study the thermodynamics of
black holes. Two interesting models are considered. One is the self-regular
Schwarzschild-AdS black hole whose mass density is given by the analogue to
probability densities of quantum hydrogen atoms. The other model is the same
black hole but whose mass density is chosen to be a rational fractional
function of radial coordinates. Both mass densities are in fact analytic
expressions of the ${\delta}$-function. We analyze the phase structures of the
two models by investigating the heat capacity at constant pressure and the
Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay
into the pure thermal radiation even with the positive Gibbs free energy due to
the existence of a minimal length. Furthermore, we extend our analysis to a
general mass-smeared form that is also associated with the ${\delta}$-function,
and indicate the similar thermodynamic properties for various possible
mass-smeared forms based on the ${\delta}$-function.
