The use of I-Core sandwich panel has increased in cruise ship deck structure since it can provide similar bending strength with conventional stiffened plate while keeping lighter weight and lower web height. However, due to its thin plate thickness, i.e. about 4~6 mm at most, it is assembled by high power $CO_2$ laser welding to minimize the welding deformation. This research proposes a volumetric heat source model for T-joint of the I-Core sandwich panel and a method to use shell element model for a thermal elasto-plastic analysis to predict welding deformation. This paper, Part I, focuses on the heat source model. A circular cone type heat source model is newly suggested in heat transfer analysis to realize similar melting zone with that observed in experiment. An additional suggestion is made to consider negative defocus, which is commonly applied in T-joint laser welding since it can provide deeper penetration than zero defocus. The proposed heat source is also verified through 3D thermal elasto-plastic analysis to compare welding deformation with experimental results. A parametric study for different welding speeds, defocus values, and welding powers is performed to investigate the effect on the melting zone and welding deformation. In Part II, focuses on the proposed method to employ shell element model to predict welding deformation in thermal elasto-plastic analysis instead of solid element model.