Several calorimetric techniques are available for the sequential estimation of thermal conductivities of composites by conducting heat balance successively along the principal directions. Such methods are time consuming and require three samples for estimating the properties. The hollow core, in combination with rigid face sheets, helps in achieving a high strength to-weight ratio, as demanded by its application. Because the manufacturing process of composites inevitably gives rise to a joint resistance between the face sheets and the core, due to the presence of an adhesive, its effect becomes detrimental in the estimation of effective thermal transport properties. A combination of several values of tridimensional effective thermal conductivities may lead to same temperature distribution; hence, the problem is ill posed in nature and requires regularization prior, an engineering intuition, or a combination of both.