As a type of powder-bed-based Additive Manufacturing (AM), Selective Laser Melting (SLM) is widely used for building metallic lattice structures. However, during SLM process, geometrical imperfections and defects, such as strut over-sizing or under-sizing, typically exist in components due to overheating, which strongly influence their mechanical response. Therefore, it is common that the as-built lattice has discrepancies from the designed lattice structure in mechanical properties. The main aim of this study is to simulate the transient temperature field of lattices during SLM process to predict the possible manufacturing issues for the improvement of product quality. Based on a technique, the moving grid method, growing struts of a lattice whilst it being built by SLM can be regarded as moving domain problems, and thermal process of a building lattice can be simulated numerically. The primary contribution of this study is to evaluate the effect of process parameters, including laser power, energy density and material deposition rate, on thermal evolution of a lattice during SLM. Another contribution is related to the comparison of transient temperature field between different lattice architectures. Analyzing the influences of various factors is important to recognize the thermal evolution of a building lattice. The results reported in this study offer a reference for quality improvement of produced parts, to realize that both geometry and mechanical properties of the as-built lattices as close as possible to their as-designed counterparts.