A carbon dust particle in a collisionless thermal plasma is studied under the assumption of the drifting Maxwellian distribution with a time varying velocity caused by the oscillatory radio-frequency (RF) field. The dust particle potential decreases while its fluctuation increases with the increasing RF field strength or the decreasing frequency even taken into account the thermionic current. As the thermionic current is increased by changing the dust particle surface temperature, the resultant increasing dust particle potential can vary from negative to positive, and the fluctuation of the dust particle potential increases first and then decreases. When the dust particle heating and mass loss processes are considered, it is found that the fluctuation of the total energy flux to the dust particle is mainly determined by the electron energy flux, which causes the stair-like increase of the dust particle surface temperature in heating process and the stair-like decrease of the dust particle radius in the mass loss process. With the increasing RF field strength or decreasing frequency, the increase of the total energy flux to the dust particle leads to the decrease of the dust particle lifetime. The results mean that the presence of the RF field can shorten the dust particle lifetime or reduce the dust particle survivability in RF plasma, by compared with in the absence of the RF field.