  The Double Green Function Formalism has been extensively used in dealing with
the thermodynamics of quantum systems which evolved in time under the action of
a given self-adjoint Hamiltonian. In this work, we extend the formalism to
include pseudo-hermitian Hamiltonians. We apply the formalism to study the
PT-symmetry Swanson Hamiltonian at finite temperature, both in the PT-unbroken
and in the PT-broken symmetry phase. We analyse the behaviour of the system,
which is initially at equilibrium at a given temperature, when it is perturbed
by a periodic interaction.
