Kinetic-theory analytical results are presented concerning the effect of intense evaporation on the thermophoretic force acting on a spherical particle suspended in a high-temperature diatomic gas for the case of free-molecule regime. Molecule dissociation and atom recombination are included in the analysis. It has been shown that evaporation may substantially enhance the thermophoretic force acting on a particle, especially for the case of the particle materials with low evaporation latent heat and small molecular weight and at high gas temperatures. The values of the effective atomic and molecular thermal-accommodation factors do not affect the thermophoretic force acting on a nonevaporating particle, but they affect significantly the evaporation-added thermophoretic force. It has been shown that the recombination fraction of atoms at the particle surface does not influence the thermophoresis.