Theoretical and analytical thermal and electrical properties are studied through the 2,7-Di([1,1′-biphenyl]-4-yl)-9H-fluorene aromatic system as a prototype of a molecular switch. Variations of the dihedral angles between the two Benzene rings at each end of the molecule have been considered, thus determining the dependence on the structural variation of the molecule when the aromatic system is connected between metal contacts. The molecule is modeled through a Tight-Binding Hamiltonian where—from the analytical process of decimation and using Green’s functions—the probability of transmission (T) is calculated by using the Fisher–Lee relationship. Consequently, the thermal and electrical transport properties such as I − V curves, quantum noise (S), Fano factor (F), electrical conductance (G), thermal conductance ( κ ), Seebeck coefficient (Q), and merit number ( Z T ) are calculated. The available results offer the possibility of designing molecular devices, where the change in conductance or current induced by a stereoelectronic effect on the molecular junctions (within the aromatic system) can produce changes on the insulating–conductive states.