The ease with which domain walls (DWs) in ferroelectric materials can be
written and erased provides a versatile way to dynamically modulate heat
fluxes. In this work we evaluate the thermal boundary resistance (TBR) of
180$^{\circ}$ DWs in prototype ferroelectric perovskite PbTiO$_3$ within the
numerical formalisms of nonequilibrium molecular dynamics and nonequilibrium
Green's functions. An excellent agreement is obtained for the TBR of an
isolated DW derived from both approaches, which reveals the harmonic character
of the phonon-DW scattering mechanism. The thermal resistance of the
ferroelectric material is shown to increase up to around 20%, in the system
sizes here considered, due to the presence of a single DW, and larger
resistances can be attained by incorporation of more DWs along the path of
thermal flux. These results, obtained at device operation temperatures, prove
the viability of an electrically actuated phononic switch based on
ferroelectric DWs