  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.
