The Metal Laser Sintering (MLS) process has been developed over the last decade to produce 3D parts from CAD files using metal powders. A considerable amount of research has been conducted into the melting and solidifying process of metal powders, mainly to predict the temperature distribution in a single metal powder layer or a few layers. The temperature and thermal residual stress distribution in real parts built using MLS has rarely been reported. Finite element simulations of temperature distributions in metal powders and parts requires huge computing resources, this is the main obstacle to successfully predicting temperature and thermal stress distributions in MLS parts. However, from the numerical results in this paper, the periodic nature of temperature distributions in parts around the laser spot can be used to simplify the numerical simulation process to achieve the prediction of temperature and thermal stresses distributions in parts built by MLS.