The transient temperature distribution of materials during upsetting forming is very important for quality of upsetted workpiece and understanding the thermal characteristics of upsetting is essential for optimum control of the forming. In this paper it is shown that the governing equation of heat transfer for axi-symetric body can be derived from minimizing a functional, and from this theory, formulation of analysis by the finite element method is presented. It is also shown that the thermal contact resistance between two bodies can be represented by equivalent coefficient of heat conductivity. Some examples of calsulated transient temperature distributions by the computer program diveloped from the theory presented in this paper are given in graphic forms. It is proven that the results calculations are very plausible.