  Ferroelectric domain walls are boundaries between regions with different
polarization orientations in a ferroelectric material. Using first principles
calculations, we characterize all different types of domain walls forming on
($11\bar{1}$), ($111$) and ($1\bar{1}0$) crystallographic planes in
thermoelectric GeTe. We find large structural distortions in the vicinity of
most of these domain walls, which are driven by polarization variations. We
show that such strong strain-order parameter coupling will considerably reduce
the lattice thermal conductivity of GeTe samples containing domain walls with
respect to single crystal. Our results thus suggest that domain engineering is
a promising path for enhancing the thermoelectric figure of merit of GeTe.
