Mitigating the structural damage brought about by thermal expansion is a primary objective in the design of vital concrete infrastructures, such as bridges or buildings. Shape memory alloys (SMAs), through their ability to recover strains through thermal loading-induced phase transformations, offer a distinct advantage in achieving this design goal as such strain recovery in embedded components could be used to oppose thermal expansion in a surrounding matrix (e.g. concrete). This study seeks to characterize the thermal expansion of system, comprised of an SMA rod embedded in a concrete block undergoing a thermal loading cycle. Characterization is produced through a full factorial analysis, wherein evaluation is performed through the Abaqus unified finite element analysis suite. This preliminary analysis indicates that, while iron-based SMAs show promise in this field due to their low manufacturing costs, their large thermal hysteresis may lead to limited phase transformation in this application.