Perturbation theory in thermofield dynamics (a real time finite temperature quantum field theory) is formulated in the interaction representation and a diagrammatic expansion for the expectation value of time ordered products is derived solely on the basis of the thermal state condition and the algebraic properties of the operators. This new formulation has a much wider domain of applicability than those presented previously. The method is applicable even in the case of purely quantum mechanical systems. When certain bosonic operators, which commute with the unperturbed Hamiltonian, contribute to the renormalization of the thermal state vacuum the vacuum diagrams do not cancel in the usual way. It will be shown how these diagrams arise and how they may be computed.