This paper presents a computationally efficient finite element analysis (FEA) approach for simulating the cladding process in surface enhancement manufacturing. The proposed method incorporates a transient heat transfer model with temperature-dependent material properties and a moving heat source described by a double Gaussian ellipsoid, following the Goldak model. The formulation accounts for convection and radiation boundary conditions, as well as phase transformation effects represented by a broadened melting interval. A dynamic mesh adaptation strategy was implemented, enabling real-time modification of the computational domain and element size according to the position of the heat source. This approach significantly reduced the computational cost while maintaining numerical stability and accuracy. The simulation results for C45 steel (1.0503) demonstrated excellent convergence, with the relative error not exceeding 0.45%. The entire simulation, performed using open-source software, confirmed that the proposed adaptive FEA framework effectively balances precision and computational efficiency in modeling thermally complex cladding processes.