  We study the energy transport between two interacting spin chains which are
initially separated, held at different temperatures and subsequently put in
contact. We consider the spin-1/2 XXZ model in the gapless regime and exploit
its integrability properties to formulate an analytical Ansatz for the
non-equilibrium steady state even at temperatures where the low-energy
Luttinger liquid description is not accurate. We apply our method to compute
the steady energy current and benchmark it both with the known low-energy limit
and at higher temperatures with numerical simulations. We find an excellent
agreement even at high temperatures, where the Luttinger liquid prediction is
shown to fail.
