In this paper, we study the thermal dissipation of Raman fiber laser and amplifier utilizing pure passive fiber as gain medium for the first time. Take into account the convective and conductive heat transferring process in the fiber, we consider the heat transferring and Raman conversion model based on the thermal conduction equations and the Raman coupled equations in the fiber. With the simulation of power distribution, the thermal profiles of Raman fiber laser are analyzed, including the transverse and longitudinal distributions of the heat load density, temperature, and thermal-induced refractive index change in the fiber. Meanwhile, the heat dissipation in multimode graded-index fiber and step-index fiber are also calculated and compared. The results show that the amplifier is superior to the resonator in heat alleviation, and the forward pumping scheme is also better to ease the thermal load than the backward and bidirectional pumping schemes, which have consult meaning for the suppression of thermal effects and the power scaling in Raman fiber lasers.