It is quite common to employ thin metallic films for the determination of heat transfer rates at a fluid-solid interface. Depending on the duration of the event and gage design, it may be important to account for multi-dimensional heat conduction within the substrate of the thin film. The objective of this work is to assess the effects of two-dimensional heat conduction on the deduced radiative heat fluxes using a conjugate-gradient based inverse algorithm. For comparison, a previously developed one-dimensional inverse technique is also used. The high heat fluxes are produced by an electrothermal-chemical plasma jet. The plasma, initiated within a 3.2 mm diameter and 26 mm long polyethylene capillary by exploding a 3.6 mg thin copper wire, emerges into an open-air atmosphere as a high-temperature, high-pressure, underexpanded supersonic jet. The jet impinges over a stagnation plate equipped with thin-film sputtered platinum heat-flux gages, whose temperature history serves as an input to the heat-flux estimation algorithm. Four different charging voltage levels are investigated, ranging from 2.5 to 7.5kV. While both algorithms capture the temporal variations of the radiative heat fluxes, two-dimensional heat conduction model reveals the discrepancies between the two techniques as well as the range of applicability of the one-dimensional model.