Temperature dependence of the polaron

We point out that the existing literature is not even clear on which direction the polaron energy should change with temperature. We analyze the existing simple calculations and show that they are most easily understood in terms of phonon-frequency shifts, rather than a temperature-dependent polaron self-energy. We show further that there are two different ways of defining a temperature-dependent polaron energy level, both of which play a role in some calculations. We use a temperature-dependent form of the intermediate-coupling theory which gives results that are qualitatively acceptable.