The spontaneous order of electric and magnetic dipoles in ferroelectrics and ferromagnets even at high temperatures is both fascinating and useful. Transport of magnetism in the form of spin currents is vigorously studied in spintronics, but the polarization current of the ferroelectric order has escaped attention. We therefore present a time-dependent diffusion theory for heat and polarization transport in a planar ferroelectric capacitor with parameters derived from a one-dimensional phonon model. We predict steady-state Seebeck and transient Peltier effects that await experimental discovery.