In this article some aspects of thermal stability for black holes is reviewed. We emphasize on how black hole solutions can be classified into equivalent topological classes, defined on the thermodynamic parameter space. Moreover, by taking into account the backreaction of a secondary hair onto the spacetime geometry, which is modified nontrivially, we derive, in a model independent way, the condition for the hairy black holes to reach a stable thermal equilibrium with the heat bath. Specifically, if the scalar hair, produces an inner horizon in the deformed geometry, a thermodynamically stable configuration will be reached. Such a mechanism might potentially produce black hole remnants from the early universe.