We report the magnetic-field dependence of thermal conductivity (kappa) of an insulating cuprate Nd_2CuO_4 at very low temperatures down to 0.3 K. It is found that apart from the paramagnetic moments scattering on phonons, the Nd^{3+} magnons can act
as either heat carriers or phonon scatterers, which strongly depends on the long-range antiferromagnetic transition and the field-induced transitions of spin structure. In particular, the Nd^{3+} magnons can effectively transport heat in the spin-flopped state of the Nd^{3+} sublattice. However, both the magnon transport and the magnetic scattering are quenched at very high fields. The spin re-orientations under the in-plane field can be conjectured from the detailed field dependence of kappa.
