Concerning a heat source model for estimating thermal cycles near the fusion line in arc welding from heat conduction theory, the details of the frame model formed by line heat segments which correspond to heat transfer due to the plasma stream and molten metal flow have been proposed and can be determined using a personal computer system designed for rough selection of line segments on the basis of expert knowledge of the weld pool and simplification for practical use, evaluation of the effect of each segment on the thermal cycle by multiple regression analysis, and checking adaptability of the segments from the distribution of the residuals and the time at a maximum temperature due to each segment. As a result, a model for a given welding condition can be obtained on the basis of data on weld penetration. A system to predict hardness and microstructural constituents in the heat affected zone and determine optimum welding conditions has been developed using an estimated thermal cycle and a CCT diagram for welding.