Semiactive vibration reduction devices using magnetorheological fluid (MR fluid) have proven to be effective in different engineering applications. MR squeeze film damper (MR-SFD) is one type of such devices that can be used to reduce unwanted vibration in rotary machinery. The behavior of these devices is a function of electric current, which controls the magnetic field in the lubricant and therefore causes the viscosity of MR fluid to be changed. In spite of all researches have been carried out in behavior analysis of different sorts of MR-SFDs, investigations over thermal growth effects on the efficiency of these actuators, in vibration reduction applications, are rare. In this paper, a Magnetorheological squeeze film damper (MR-SFD) has been modeled using two governing equations. First, considering the Bingham model for MR fluid (MRF), a hydrodynamic model has been presented. Second, a thermal model for the system has been modeled and used to calculate the temperature rise in the squeeze film and different damper’s components. Temperature rise in MR-SFD has been considered in this paper as a novel study. Time and frequency domain analysis using Newmark method has been performed over a finite element model of the system consisting of an unbalanced flexible rotor mounted on a pair of MR-SFDs. Obtained results show that the amplitude of rotor’s vibration is not a simple function of electrical current such that, increase in the current cannot guarantee decrease in the value of amplitude. Two major phenomena have been observed during studies; rigid dampers, and generation of new critical speed. The behavior of the rotor is deeply affected by these phenomena. The steady state response of rotor versus rotation velocity is presented for different values of electrical current, which show the effects of temperature and current on the steady state response of rotor. Generally, temperature rise results in inefficiency of MR-SFDs to suppress the vibration of the rotor, especially for rotational velocities near critical speed. Due to temperature rise, appearance of the second critical speed occurs at higher values of electrical current. In addition, it delays the “rigid damper” phenomenon causing rotor response to decrease.