This paper presents a new method for the multidimensional reconstruction of the heat flux via distributed surface temperature measurements and its validation using hypersonic wind tunnel tests. The first innovation is the formulation of the reconstruction in terms of the Green’s function, approximated using a weak Galerkin technique together with the method of variation of parameters. When compared with previous research, the method does not require nullification of the first derivative of the polynomial basis at boundaries of the second kind, and it applies seamlessly to complex geometries. The second innovation is the use of homotopy to reduce the nonlinear conduction at high temperature to a series of linear subproblems. Our main contribution is the determination of the conditions for the quadrature formulas to yield a convergent homotopy sequence. The third innovation is the use of a multidimensional B-spline basis to reconstruct the heat flux on curved surfaces and in time. The inverse problem projected in the B-spline basis is well-posed and does not require regularization parameters. The fourth innovation is the introduction of a piecewise Green’s function on partitioned multimaterial domains by imposing continuity of heat flux and temperature. The partitioned approach improves the accuracy of the reconstruction in the linear and nonlinear regimes.