Solidification is a key step in additive manufacturing technology because it determines the microstructure and performance of the final product. Our work provides the nanoscale description of relevant solidification processes for polycrystalline Ni by means of molecular dynamics simulations. In particular, we focus on the thermal effects associated with the characteristic non-stationary conditions of additive manufacturing. Directional solidification and homogeneous nucleation are investigated as a function of operating parameters that control the temperature gradient and the cooling rate. We show that a planar solid/liquid interface propagates at a constant speed, in the presence of a temperature gradient between the melt pool and the solidified region. By adding cooling to the melt pool, a columnar-to-equiaxed transition can be captured at the nanoscale. If the undercooling is not sufficient to promote nucleation, a strong instability of the interface develops, forming protusions. The behaviors observed at the nanoscale are interpreted in terms of the classical theories of solidification and nucleation.