The goal of this work is to achieve a novel solution of the transient heat transfer problem in the start-up phase of directchill casting processes using a Generalized Finite Differences Method. This formulation is applied in order to solve the heat transfer equation in strong form under a Lagrangian description. The boundary conditions incorporation is done in a simple and natural way. The meshfree nature of this approach allows to capture the motion and phase boundaries evolution without using remeshing approaches. The simplicity, efficiency and suitability of this numerical formulation is demonstrated by comparison of the obtained numerical results with the results already published by other researchers. This shows that our approach is promising for the numerical simulation of heat transfer problems during the start-up phase of direct-chill casting processes. nema