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We present exact results on the thermal conductivity of the one-dimensionalspin-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 asanalytical results in the low and high temperature limits are presented. Atfinite temperature, the thermal Drude weight is finite and hence there isnon-dissipative thermal transport even in the massive regime. At lowtemperature, the thermal Drude weight behaves as $D(T)\sim\exp(-\delta/T)/\sqrt{T}$ where $\delta$ is the one-spinon (respectivelyone-magnon) excitation energy for the antiferromagnetic (respectivelyferromagnetic) regime.Comment: 16 page

Non-dissipative thermal transport in the massive regimes of theXXZchain