  In this Letter we study interacting systems with spontaneous discrete
symmetry breaking, where the degenerate symmetry-broken states are
topologically distinct gapped phases. Edge modes appear at domain walls between
the two topological phases. In the presence of a weak disorder field conjugate
to the order parameter, we find that the entropy of the edge modes drives a
thermal transition between a gapped uniform phase and a phase with a
disorder-induced domain structure. We characterize this transition using a
phenomenological Landau functional, and corroborate our conclusions with a
concrete microscopic model. Finally, we discuss the possibilities of
experimental signatures of this phase transition, and propose graphene-based
moir\'e heterostructures as candidate materials in which such a phase
transition can be detected.
