  We study the finite-temperature transport of electrons coupled to anharmonic
local phonons. Our focus is on the high-temperature incoherent regime, where
controlled calculations are possible both for weak and strong electron--phonon
coupling. At strong coupling, the dynamics is described in terms of a
multiple-species gas of small polarons: this emergent `speciation' is driven by
energy conservation. We explicitly compute the dc and ac response in this
regime. We discuss the breakdown of the polaron picture, and the onset of
localization, in the limit where phonons become quasistatic.
