During the operation of magnetorheological (MR) dampers, the temperature rise can significantly affect their damping performance. Therefore, aiming at reducing the operating temperature of MR damper, this study proposed a circular ring ribbed heat dissipation structure and analyzed its heat transfer enhancement effect based on the multi-physics coupling method. A theoretical model for the temperature rise of the MR damper is established by using the simplified one-dimensional heat transfer model of the fluid element. Additionally, a quasi-static mechanical model of the MR damper and a fin heat transfer model are also established. A multi-physics coupled model of MR damper was established in the finite element analysis software. Temperature rise characteristics and fin heat transfer performance were analyzed. The simulation results demonstrate the existence of a temperature gradient along the piston axis in the MR fluid within the MR damper, with the damping gap region showing the most rapid temperature rise rate, highest equilibrium temperature, and smallest temperature differential. The temperature rise rate of the MR fluid is positively correlated with the excitation current. The proposed structure effectively reduces both the temperature rise rate and peak equilibrium temperature of the MR damper.