The authors have accomplished to extend the logic of the Finite Element Method to the principle of Thermal Forming or Line Heating so as to facilitate creating curvature effectively on a hull steel plate by using fully automated, revolutionized line heating system in shipbuilding process. This paper writes of the elaboration on the development of the line heating unit. The elastic calculation based on the theory of inherent strain makes design of heating process plans available in reasonable time, though the forming by line heating consists of thermal conduction and thermal-elastic-plastic phenomena. The result of experiments on precise forming for saddle shape by stepping heat source travel was presented in the previous report. Succeedingly, this paper states the followings : (1) a calculation method for designing heating process plans with use of continuous traveling heating which is more practical in view of operation. (2) the results of quantitative analysis on the factors which affect thermal deformation, e. g. residual stress. (3) what actually happened at experiments with experimental apparatus in consideration of the above study results. Further, the realization of the first, fully automated line heating unit for actual steel forming work process in shipbuilding, being considered the above, ought to be completed in the near future.