Heat transfer in directed energy deposition (DED) is governed by component geometry. To achieve repeatable and high-quality DED repair, the geometry-dependent thermal responses need to be fully understood. However, the existing studies either relied on a conduction-only assumption or did not examine the evolution of heat flow across varying component thicknesses. In this work, we combine in-situ coaxial thermal monitoring with a numerical model based on the finite element method to investigate the thermal responses of 9 DED-fabricated Inconel 718 structures, varying from thin- to thick-wall regimes. The analyses of the average temperature in the melt pool reveal a non-linear relationship between thermal intensity and wall thickness, characterized by an initial increase followed by a decrease. For explanation, the total heat loss and the relative contribution of conductive, convective, and radiative heat loss are quantified. The results demonstrate that, as the wall thickness increases from 1.1 mm to 9.1 mm, the total heat losses also follow a non-monotonic trend. The minimum total heat loss occurs in the wall featuring a thickness of 2.1 mm, which coincides with the wall having the peak average thermal intensity. Meanwhile, heat conduction is the dominant heat transfer mechanism across all geometries; however, convective and radiative heat losses increase as the wall thicknesses decrease, due to the higher surface-to-volume ratio of the melt pool in thinner walls that enhances both convection and radiation cooling. Moreover, once the wall thickness exceeds 4 mm, the total heat loss stabilizes, with the relative contribution of conductive heat losses accounting for more than 80% of the heat dissipation in the melt pool. This indicates that, under the given deposition conditions, walls thicker than 4 mm exhibit bulk-like thermal behavior, for which conduction-dominated assumptions remain valid in thermal analyses.