  We present exact results on the thermal conductivity of the one-dimensional
spin-1/2 XXZ model in the massive antiferromagnetic and ferromagnetic regimes.
The thermal Drude weight is calculated by a lattice path integral formulation.
Numerical results for wide ranges of temperature and anisotropy as well as
analytical results in the low and high temperature limits are presented. At
finite temperature, the thermal Drude weight is finite and hence there is
non-dissipative thermal transport even in the massive regime. At low
temperature, the thermal Drude weight behaves as $D(T)\sim
\exp(-\delta/T)/\sqrt{T}$ where $\delta$ is the one-spinon (respectively
one-magnon) excitation energy for the antiferromagnetic (respectively
ferromagnetic) regime.
