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In this paper we consider the heat transfer properties of the axially symmetric body with parabolic shape at hypersonic speeds (with a Mach number M > 5). We use the numerical methods based on the implicit difference scheme (Fedorenko method) with direct method based on LU-decomposition and iterative method based on the Gauss-Seigel method. Our numerical results show that the heat removing process should be performed in accordance with the nonlinear law of heat distribution over the surfacedoi:10.1051/matecconf/20168307004 fatcat:avd362qdxfdmdigd63ehnnk4ua