Using continuum elasticity theory, we investigate the stability of coexisting 7x7 and '1x1' phases on Si(111) as a function of temperature. We find that of the many possible 'droplet' phases, a configuration in which triangular domains meet corner-to-side is the most stable. At fixed separation, the elastic interaction between two domains is minimized in the corner-to-side arrangement. Away from the transition temperature, the size of the domains decreases while the domain spacing diverges.