In this study, a novel "divide and conquer" approach is applied to estimate the principal thermal conductivities of an orthotropic material, specifically engineered with a view to demonstrate the potency of the inverse heat transfer method with unsteady temperature data. Electro discharge machining (EDM) is used to carve out cavities from a solid SS304 plate to engineer the sample with orthotropic conductivities. The sample is placed in a vacuum chamber maintained at a pressure of 0.00000086 mbar. Unsteady experiments for four heat fluxes cases were carried out and temperatures at time instants of 5, 15, 25 min were measured with T-type thermocouples. The corresponding forward model simulations for the forward three dimensional, unsteady orthotropic conduction model were done with COMSOL . The heat capacity of the engineered orthotropic material was determined by first estimating the heat capacity of a solid block of SS304 with identical boundary conditions as the orthotropic material in a sequential fashion. First steady-state experiments followed by a Bayesian estimation with the Metropolis Hastings (MH) based Markov Chain Monte Carlo (MCMC) method were done to obtain the thermal conductivity of a solid SS304 block. Using this as a prior, the heat capacity of solid SS304 block was obtained through unsteady experiments followed by Bayesian estimation with MCMC method. The heat capacity of SS304 thus obtained is multiplied by the solidity of the engineered orthotropic material to estimate its three components of the orthotropic conductivity again using Bayesian route. To expedite the estimation, a surrogate for the forward model was developed using artificial neural network. Three points estimators, namely the mean, maximum a posteriori (MAP), and the standard deviation of the estimates, are reported. Finally, the retrieved parameters are used to determine the simulated temperatures through the forward model for the orthotropic material. These, when compared with the measured temperatures, gave excellent agreement.