The notion of (static) solvation shells has recently proved fruitful in revealing key molecular factors that dictate the solubility and aggregation properties of fullerene species in polar or ionic solvent media. Using molecular dynamics schemes with carefully evaluated force fields, we have scrutinized both the static and the dynamic features of the solvation shells of single C-60 particle for three nonpolar organic solvents (i.e., chloroform, toluene, and chlorobenzene) and a range of system temperatures (i.e., T = 250-330 K). The central findings have been that, while the static structures of the solvation shell remain, in general, insensitive to the effects of changing solvent type or system temperature, the dynamic behavior of solvent molecules within the shell exhibits prominent dependence on both factors. Detailed analyses led us to propose the notion of dynamically stable solvation shell, effectiveness of which can be characterized by a new physical parameter defined as the ratio of two fundamental time constants representing, respectively, the solvent relaxation (or residence) time within the first solvation shell and the characteristic time required for the fullerene particle to diffuse a distance comparable to the shell thickness. We show that, for the five (two from the literature) different solvent media and the range of system temperatures examined herein, this parameter bears a value around unity and, in particular, correlates intimately with known trends of solubility for C-60 solutions. We also provide evidence revealing that, in addition to fullerene solvent interactions, solvent solvent interactions play an important role, too, in shaping the dynamic solvation shell, as implied by recent experimental trends.