  Topological entanglement entropy is a topological invariant which can detect
topological order of quantum many-body ground state. We assume an existence of
such order parameter at finite temperature which is invariant under smooth
deformation of the subsystems, and study its stability under hamiltonian
perturbation. We apply this assumption to a Gibbs state of hamiltonian which
satisfies so called `strong commuting' condition, which we shall define in the
paper. Interesting models in this category include local hamiltonian models
based on quantum error correcting code. We prove a stability of such
topologically invariant order parameter against arbitrary perturbation which
can be expressed as a sum of geometrically local bounded-norm terms. The first
order correction against such perturbation vanishes in the thermodynamic limit.
