In this paper, we are interested in flexible modeling and performing solution of transient thermal Selective Laser Melting Problems. For this, we first introduce a Finite Addition of Matter Elements Method (FAMEM) to generate any wished finite sequence of thermal problems, defined in additively constructed domains. Second, we use the Multiscale Arlequin Frame-work to develop a three-level Arlequin weakstrong formulation of each problem of the finite sequence. Two Arlequin patches are used in the latter to localize the steepest thermal gradients and the nonlinear phase-change phenomena, allowing for fine local approximations and the localized nonlinearity treatment by an algorithm we develop. These patches are identified via the solution of a representative mono-domain transient thermal problem. The latter is also solved with our three-Level Arlequin method for comparison of the solutions and respective performances of both approaches.Moreover, two dimensional tests consisting in the creation of a 316 L stainless steel wall and a two AlSi10Mg layers, are carried out to further enlighten our global approach and to position it with respect to literature.