Extractive dividing-wall column (EDWC) was proved to be a promising energy-saving technique for the separation of multiple azeotropes or close-boiling mixtures; however, its controllability is very challenging due to its intensified structure with smaller physical space and strong interactions. Most studies on the EDWC control focused on evaluating the performance of temperature or composition control using proportional-integral (PI) control; nevertheless, significant steady-state offsets and overshoots are present in the control of two product purities of EDWC under different disturbances. In this paper, the performance of single temperature control (TC), temperature difference control (TDC) and double temperature control (DTDC) schemes for PI control of EDWC was first examined for the separation of toluene and 2-methoxyethanol using dimethyl sulfoxide as the entrainer. The results show that the steady-state offsets in product purities of TDC scheme are much smaller than those of TC and DTDC schemes. Subsequently, the offset-free model predictive control (MPC) based on temperature differences was proposed to improve the operation of EDWC. The results indicate that this MPC scheme can achieve much better control performance than PI control in terms of maximum transient deviation, amplitude of oscillations and setting time.