The improvement of both heat recovery Joule-Brayton cycles and closed cycle (externally fired) gas turbine plants is strongly limited by the availability of high efficiency heat exchangers. In such a scenario, a nonconventional heat exchanger was recently proposed; this device employs falling solid particles to perform heat transfer between two separate gas flows and was designed with a 1D model neglecting conduction within the particles. Although the experimental reliability of this assumption was already obtained for one particle size, there is no proof available of the quantitative effect introduced by the above mentioned simplification and, more importantly, no indication of when this assumption becomes unacceptable. In this work, direct numerical simulation (DNS) of a solid particle immersed in a gas flow has been performed in order to further validate the hypothesis of negligible conduction and to enhance the design of the proposed heat exchanger. Unsteady conjugate heat transfer has been used to predict the final temperature of the solid sphere for Reynolds numbers ranging from 30 to nearly 300, the computational grid being generated with the immersed boundary (IB) technique. A validation of the study is presented, together with grid independence and boundary independence assessment. The results fully confirmed the worthiness of the initial assumption, with a 1.4% maximum error for high Reynolds conditions (large diameter particles) with respect to the 1D model. Additionally, the code has been employed to explore the influence of the wake in the case of aligned particles, namely, the worst possible situation in terms of efficiency of the heat transfer mechanism. Finally, the discrepancy between the results obtained with an axisymmetric domain and a 3D domain, in terms of final temperature of the particle, have been investigated for the highest Reynolds number, when the flow is supposed to lose its axial symmetry.