This article shows experimentally that an external electric field affects the velocity of the longitudinal acoustic phonons ( v _LA ), thermal conductivity (κ), and diffusivity ( D ) in a bulk lead zirconium titanate–based ferroelectric. Phonon conduction dominates κ, and the observations are due to changes in the phonon dispersion, not in the phonon scattering. This gives insight into the nature of the thermal fluctuations in ferroelectrics, namely, phonons labeled ferrons that carry heat and polarization. It also opens the way for phonon-based electrically driven all-solid-state heat switches, an enabling technology for solid-state heat engines. A quantitative theoretical model combining piezoelectric strain and phonon anharmonicity explains the field dependence of v _LA , κ, and D without any adjustable parameters, thus connecting thermodynamic equilibrium properties with transport properties. The effect is four times larger than previously reported effects, which were ascribed to field-dependent scattering of phonons.