Additional kinetic-theory analytical results are presented concerning the thermophoretic force acting on a spherical nonmetallic or metallic, nonevaporating or evaporating particle suspended in a plasma for the extreme case of free-molecule regime and thin plasma sheath. A combined specular and diffuse reflection of the atoms incident on or formed in the ion-electron recombination process at the particle surface has been taken into account in this analysis as an extension of the the previous paper (Xi Chen, J. Phys. D: Appl. Phys. 30, 826-841, 1997). It has been shown that the specular reflection fraction of gas particles at the surface does not affect the thermophoretic force acting on a nonevaporating, metallic or nonmetallic, spherical particle, but they affect significantly the evaporation-added thermophoretic force. The evaporation-added thermophoretic force decreases linearly with the increase of the specular reflection fraction, and the decreasing rate for a nonmetallic evaporating particle is much greater than that for a metallic one at high plasma temperatures.