  We study topological order in a toric code in three spatial dimensions, or a
3+1D Z_2 gauge theory, at finite temperature. We compute exactly the
topological entropy of the system, and show that it drops, for any
infinitesimal temperature, to half its value at zero temperature. The remaining
half of the entropy stays constant up to a critical temperature Tc, dropping to
zero above Tc. These results show that topologically ordered phases exist at
finite temperatures, and we give a simple interpretation of the order in terms
of fluctuating strings and membranes, and how thermally induced point defects
affect these extended structures. Finally, we discuss the nature of the
topological order at finite temperature, and its quantum and classical aspects.
