The warm shrink fitting process is generally used to assemble automobile transmission parts (shafts/gears). However, this process causes a deformation in the addendum and dedendum of the gear depending on the fitting interference and gear profile, and this deformation causes additional noise and vibration between the gears. To address these problems, the warm shrink fitting process is analyzed by considering the error in the dimensional deformation of the addendum and dedendum found when comparing the results of a theoretical analysis and finite element analysis (FEA). A correction coefficient that reduces this error is derived through an analysis of the difference in the cross-sectional area between the shapes used for the theoretical analysis and that of the actual gear, and a closed-form equation to predict the dimensional deformation of the addendum and dedendum is proposed. The FEA method is proposed to analyze the thermal-structural-thermal coupled field analysis of the warm shrink fitting process (heating-fitting-cooling process). To verify the closed-form equation using the correction coefficient, measurements are made of actual helical gears used in automobile transmissions. The results are in good agreement with those given by the closed-form equation.