  Quantum impurity models play an important role in many areas of physics from
condensed matter to AMO and quantum information. They are important models for
many physical systems but also provide key insights to understanding much more
complicated scenarios. In this paper we introduce a simplified method to
describe the thermodynamic properties of integrable quantum impurity models. We
show this method explicitly using the anisotropic Kondo and the interacting
resonant level models. We derive a simplified expression for the free energy of
both models in terms of a single physically transparent integral equation which
is valid at all temperatures and values of the coupling constants.
