  The low thermal conductivity of piezoelectric perovskites is a challenge for
high power transducer applications. We report first principles calculations of
the thermal conductivity of ferroelectric PbTiO$_3$ and the cubic nearly
ferroelectric perovskite KTaO$_3$. The calculated thermal conductivity of
PbTiO$_3$ is much lower than that of KTaO$_3$ in accord with experiment.
Analysis of the results shows that the reason for the low thermal conductivity
of PbTiO$_3$ is the presence of low frequency optical phonons associated with
the polar modes. These are less dispersive in PbTiO$_3$, leading to a large
three phonon scattering phase space. These differences between the two
materials are associated with the $A$-site driven ferroelectricity of PbTiO$_3$
in contrast to the $B$-site driven near ferroelectricity of KTaO$_3$. The
results are discussed in the context of modification of the thermal
conductivity of electroactive materials.
