Full and partial penetration welding using high power lasers exhibit different melt pool geometries. The main difference is that full penetration welds tend to widen at the root side. In recent years, full penetration laser welding has been modeled using sophisticated multiphase numerical models. However, less computationally-complex thermo-mechanical models that are capable of accounting for the root widening phenomenon in full penetration laser welding are lacking. In this study, hybrid laser welding was performed for full and partial penetration modes on butt joints of structural steel. A numerical model was presented that used a three-dimensional transient Finite Element (FE) analysis and thermal conduction heat transfer for calculating the temperature fields in both full and partial penetration welding modes. For this purpose, a double-conical volumetric heat source was developed based on the three-dimensional conical (TDC) heat source in the literature. The model was validated and calibrated with different experiments. The results show that the model is capable of calculating the transient temperatures for the common melt pool geometries obtainable by the full and partial penetration hybrid laser welding of thick-section steels. The model can potentially be employed as the basis for predicting e.g. microstructural properties or residual stresses for a given welding procedure.