  We compare two effective phonon theories, which have both been applied
recently to study heat conduction in anharmonic lattices. In particular, we
study the temperature dependence of the thermal conductivity of the
Fermi-Pasta-Ulam model via the Debye formula, showing the equivalence of both
approaches. The temperature for the minimum of the thermal conductivity and the
corresponding scaling behavior are analytically calculated, which agree well
with the result obtained from nonequilibrium simulations. We also give quantum
corrections for the thermal conductivity from quantum self-consistent phonon
theory. The vanishing behavior at the low temperature regime and the existence
of an umklapp peak are qualitatively consistent with experimental studies.
