The evolution of C-60(111) in-plane structures is investigated on Au(111) substrates for temperatures ranging from similar to 120 to 290 degrees C. An epitaxial orientational reordering is observed at T-o similar to 150 degrees C. At temperatures TT-o, no in-phase structures are observed, but commensurate (R30.0) structures form. The majority phase, consists of structures double-positioned in the plane (+/-R13.0-14.2) with respect to the close-packed directions of the twinned commensurate structures. These double-positioned structures require large coincident unit cells to lattice-match to nonreconstructed Au(111) substrates, and with increasing temperature, the in-plane orientations of these structures change from similar to +R13.0 to +/-R14.2. The in-phase (R0.0) and commensurate (R30.0) structures do not show any dependence on the substrate temperature, nor substrate's structural quality. The in-plane orientational reordering at T-o is attributed to the surface structural instability/reconstruction of the topmost layer of the Au(111) substrate.