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It is shown that the Bethe ansatz formulation of the easy-plane 1D Heisenbergmodel thermodynamics (TBA) by Takahashi and Suzuki and the subsequent analysisof the spin Drude weight, also reproduces the thermal Drude weight andmagnetothermal coefficient obtained by the Quantum Transfer Matrix method(QTM). It can also be extended to study the far-out of equilibrium energycurrent generated at the interface between two semi-infinite chains held atdifferent temperatures.

A TBA description of thermal transport in the XXZ Heisenberg model