  We present a temperature and magnetic field dependence study of spin
transport and magnetothermal corrections to the thermal conductivity in the
spin S = 1/2 integrable easy-plane regime Heisenberg chain, extending an
earlier analysis based on the Bethe ansatz method. We critically discuss the
low temperature, weak magnetic field behavior, the effect of magnetothermal
corrections in the vicinity of the critical field and their role in recent
thermal conductivity experiments in 1D quantum magnets.
