  We provide a proof that entanglement of any density matrix which block
diagonal in subspaces which are disjoint in terms of the Hilbert space of one
of the two potentially entangled subsystems can simply be calculated as the
weighted average of entanglement present within each block. This is especially
useful for thermal-equilibrium states which always inherit the symmetries
present in the Hamiltonian, since block-diagonal Hamiltonians are common as are
interactions which involve only a single degree of freedom of a greater system.
We exemplify our method on a simple Hamiltonian, showing the diversity in
possible temperature-dependencies of Gibbs state entanglement which can emerge
in different parameter ranges.
