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The calculation of thermal boundary conditions occurring during heat treatment processes is an essential requirement for characterization of heat transfer phenomena. In this work, the performance of four different optimization methods (Conjugate Gradient Method, the Levenberg-Marquardt Method, the Simplex method and the NSGAII algorithm) is investigated. The models are used to estimate the heat transfer coefficient in 2D axis symmetrical case during transient heat transfer. The performance of the optimization methods is demonstrated using numerical experiments.