Similar to the case of symmetry breaking order, thermal fluctuations at finite temperatures can reduce or destroy the quantum correlations necessary for topological order. Once again, localization can enable such orders in regimes forbidden by equilibrium. This happens for both the so-called long range entangled topological phases, and for symmetry protected or short-range entangled topological phases. The toric-code / Z 2 gauge theory in 2D is an example of the former, and the topological order in this phase can be diagnosed by Wilson loop operators. The topological order is destroyed in equilibrium at any finite temperature due to fluctuating vortices--- however, these can get localized by disorder, enabling glassy localization-protected topological order at finite energy densities. On the other hand, symmetry protected topological (SPT) phases do have any bulk long-range order, and are distinguished from trivial paramagnets due to the presence of coherent gapless edge modes as long the protecting symmetry is present. In equilibrium, these edge modes are typically destroyed at finite temperatures as they decohere due to interactions with delocalized bulk excitations. Once again, localization protects the coherence of these modes even at finite energy densities! The presence of localization-protected topological order could potentially have far-reaching consequences for developing new quantum technologies by allowing for quantum coherent phenomena at high energies.