The six termination temperatures associated with the ten characteristic curves of a simple fluid are calculated for the Kihara potential second virial coefficient, constructed from a Lennard-Jonesm, npotential augmented by a spherical hard-core. Extreme values of the termination temperatures in both the hard-core Sutherland-type potential limitn→ ∞, and in the opposite limitn→mare obtained. Over the useful range of values, 0 to 1, of the ratioa* of the hard-core diameter to the molecular diameter in the absence of a hard-core, the termination temperature ratiosTC/TF/TCandTD/TAvary only slightly, for a given value ofn, withTD/TA→ 2 in the hard-core limitn→ ∞, independent ofmanda*.