This work reports the results of a study envisaged to benchmark a novel technique for simultaneously estimating the principal thermal conductivities (kx, ky and kz) of an anisotropic composite medium. The technique essentially involves solving a formulated Inverse Heat Conduction Problem (IHCP) using measured temperature data as input to simultaneously estimate the constant thermal conductivities along the three directions of an anisotropic composite. The IHCP is solved using a hybrid optimization algorithm where the forward simulations are driven by a carefully chosen ANN and the optimization part is accomplished by employing GA. Before accomplishing estimation with actual \measurements"synthetically generated \surrogate temperatures are used to ascertain the adequacy and robustness of the methodology. An indigenously designed anisotropic material whose effective thermal conductivities in the principal directions are determined using a full scale computational heat transfer analysis is used as a benchmark for validating the technique.