We have investigated the nanotribological properties of C-60 single crystal (111) and (100) surfaces around its orientational order-disorder phase transition temperature, similar to 260 K, by atomic force microscopy and frictional force microscopy (AFM/FFM) in high vacuum. Results show that for both surfaces across the phase transition temperature, the friction force and the adhesive force between a C-60 coated AFM tip and the C-60 crystal surfaces exhibit discontinuous behavior. The friction force within the applied external load range in the low temperature phase is significantly larger than that in the high temperature phase, with no obvious change in the slope of the friction force curves (the friction coefficient) in the low and high temperature phases. The abrupt change in friction was found to be caused mainly by the abrupt change in adhesion, which, in turn, can be qualitatively understood through changes in the van der Waals interaction and the short-range Coulomb interaction associated with the structural changes across the phase transition. Compared to most other degrees of freedom, the rotation of C-60 molecules was found to have little effect on friction and is an ineffective energy dissipation channel.