We report the temperature and magnetic field dependence of the in-plane thermal conductivity (kappa(ab)) of high-quality monocrystalline Nd2CuO4. Isothermal measurements of the field dependence of kappa(ab) at low temperatures (2 K<or=T<or=5 K) show no change in kappa(ab) below a critical magnetic field H(c) (H(c) approximately 4.5 T for H parallel [100]) and H(c) approximately 2.5 T for H approximately parallel [110]). Above H(c), kappa(ab) more than doubles as H is increased to 9 T. At H(c), there is a transition from a noncollinear to a collinear arrangement of the Nd and Cu spins and a collapse of the gap, Delta, in an acoustic magnon branch at k=0. Closure of this gap appears to allow the conduction of substantial amounts of heat by acoustic magnons.