To learn how the structures of clusters evolve as their sizes increase and how the results depend upon temperature, a program of Monte Carlo computations was begun. The program was initiated to elucidate the mechanisms by which one is able to control the phase of large clusters generated by the condensation of vapor in supersonic flow. In the present paper it was found for very small aggregates that 13-molecule, icosahedral clusters enjoy the special stability also observed for argon but not for TeF6 clusters. Even though the total stabilization per benzene molecule is greater for 13 molecules than for the average of 12 and 14, the stabilization per intermolecular contact is lower than in both the 12- and 14-molecule clusters. The low-temperature structures agreed in gross architecture with the C-3 structures reported by Williams and by van de Waal insofar as their icosahedral motifs are concerned. In detail, however, the molecules in our clusters assumed quite different orientations, leading to a lower overall symmetry. This difference is a consequence of the different intermolecular interactions adopted for the computations, our potential function having been developed specifically to account for benzene dimers. Published resonant two-photon ionization (R2PI) spectra of the 13-molecule cluster demand a lower symmetry than C-3, evidence that supports the use of the present potential function for clusters, as well. Amplitudes of molecular oscillations were determined and compared with experimental values for benzene crystals. As the temperature increased, amplitudes increased regularly until, at 85 K, our 13-molecule cluster began to execute rapid transitions between three equivalent isomers, making the superposition of the isomers resemble the more symmetric static structure of Williams. Effects of continued heating until a melting-like transition occurred are described in the next paper of this series.