  Motivated by recent experimental findings, we study the contribution of a
quantum critical optical phonon branch to the thermal conductivity of a
paraelectric system. We consider the proximity of the optical phonon branch to
transverse acoustic phonon branch and calculate its contribution to the thermal
conductivity within the Kubo formalism. We find a low temperature power law
dependence of the thermal conductivity as $T^{\alpha}$, with $1 < \alpha < 2$,
(lower than $T^3$ behavior) due to optical phonons near the quantum critical
point. This result is in accord with the experimental findings and indicates
the importance of quantum fluctuations in the thermal conduction in these
materials.
