I am examining the temperature dependence of electron phonon scattering in the case of a metal responding to an AC field (forming a plasma oscillation). I have found that for DC transport, the temperature dependence of electron phonon scattering scales as $T^5$ at low temperatures and as $T$ at high temperatures.
However, I am unsure if the same temperature dependence would hold for the AC case and if so, why it would hold?
Thank you in advance
(Source: Ziman, Electrons and Phonons, 1960)