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This article investigates the applicability of the Green-Galerkin method in problems of multi-dimensional inverse heat conduction. Several simulations are conducted to prove that despite the complexities that arise from the distributed parameter nature of the system, the aforementioned method successfully solves for the surface heat input distribution necessary to achieve a desired temperature field within the volume of a solid. FEA simulations are used to validate the analytical results obtained by Green-Galerkin algorithm. The efficiency of the method when addressing higher dimensionality problems is also investigated and addressed.