The root 3 x root 3R30 degrees-alpha surface phase of Sn/Ge(lll) transforms reversibly upon cooling into a 3 x 3 phase. Using high-resolution photoemission, the effect of this transition on the Sn core-level and the Fermi surface (FS) has been determined. The topology of the FS show a Fermi momentum along T (K) over bar and T (M) over bar of 0.27 +/- 0.02 Angstrom(-1) and 0.30 +/- 0.02 Angstrom(-1), respectively. In the low-temperature phase, a well-resolved core-level splitting is observed for the Sn adatoms. Our data are consistent with a local-bonding representation, when the transition is driven by freezing of dynamic fluctuations of two inequivalent types of Sn adatoms, coexisting at room temperature.