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This paper focuses on analytical methods of a finite-element method (FEM)-based edge heating system. The edge heating system plays a role in maintaining the temperature in the hot rolling process of carbon steel. Carbon steel moves along the production line and maintains the temperature by the edge heating system in the process. Power-of-the-edge heating system is transmitted to carbon steel during the process. Eddy currents are generated in carbon steel by Faraday’s law of electromagnetic induction, and eddy current loss serves as a heat source to increase the temperature. Thus, there is a need for accurate electromagnetic-field analysis and thermal analysis because the eddy current path generated in carbon steel greatly affects the heat distribution in carbon steel. This multiphysics analysis requires high reliability. Accordingly, this paper presents a coupling analysis method using an FEM-based coordinate mapping method as a more accurate analytical method. This paper also established an analytical approach to the edge heating system using the ductility analytical method of this coordinate mapping method. [ABSTRACT FROM AUTHOR]