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The problems of calculating non-steady temperature fields, in complex shaped axi-symmetric bodies in the processes of plastic forming as well as in working processes of ICE are concerned. A mixed method of solving this problem is proposed. According to this method, an axis section region of a complex shaped body is mapped conformally into a rectangle. A reduced boundary value problem for heat transfer is solved in this rectangle. The numerical method of a time-depending heat transfer modelling at the forming processes of impeller disk of a gas turbine is concerned.