In this study, a memristor-based 2-DOF PI controller (2-DOF Mem-PI) was designed for the temperature profile tracking control of a heat flow experiment (HFE) setup. A simulation study is presented in which the performance of the designed controller is compared with a standard 2-DOF PI controller. Compared to 1-DOF control structures, 2-DOF controllers that include an extra adjustable parameter perform better in terms of response to disturbances and improving the transient response of the system. In addition, memristor-based controllers (Mem-PI and 2-DOF Mem-PI) and standard controllers (PI and 2-DOF PI) were compared and it was determined that because of the variable memristance value, the control structures containing memristors showed an adaptive feature. The simulation results demonstrated the success of the proposed controller in temperature profile reference tracking and showed the memristor to be applicable in nonlinear control structures.