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We discuss thermodynamical stability for hairy black hole spacetimes, viewed as defects in the thermodynamical parameter space, taking into account the backreaction of a secondary hair onto the spacetime geometry, which is modified non trivially. We derive, in a model independent way, the conditions for the hairy black hole with the secondary hair to reach a stable thermal equilibrium with the heat bath. Specifically, if the scalar hair, induced by interactions of the matter fields with quadratic-curvature corrections, produces an inner horizon in the deformed geometry, a thermodynamically stable configuration will be reached with the black hole becoming extremal in its final stage. We also attempt to make some conjectures concerning the implications of this thermal stability for the existence of a minimum length in a quantum space time. Contents I. Introduction 1 II. Black Holes in a Thermal Bath and Stability Arguments 3 III. Black Holes as Thermodynamical Topological Defects 6 IV. Back Reaction of Secondary Hair and Black Hole Thermodynamical Stability 8 A. Stable Black Holes with Secondary Hair 8 B. Black Hole stability and a potential minimum length in quantum spacetime 12 V. Conclusions and Outlook 14 References 15