  We investigate the harmonic and anharmonic contributions to the phonon
spectrum of lead telluride, and perform a complete characterization of how the
anharmonic effects dominate the phonons in PbTe as temperature increases. This
effect is the strongest factor in the favorable thermoelectric properties of
PbTe: an optical-acoustic phonon band crossing reduces the speed of sound and
the intrinsic thermal conductivity. We present the detailed temperature
dependence of the dispersion relation and compare our calculated neutron
scattering cross section with recent experimental measurements. We analyze the
thermal resistivity's variation with temperature and clarify misconceptions
about existing experimental literature. This quantitative prediction opens the
way to phonon phase space engineering, to tailor the lifetimes of crucial heat
carrying phonons.
