This paper focuses on designing a controller to regulate the temperature of a horizontal metal bar with varying thermal conductivities by manipulating the heat flux. To this end, the governing partial differential equations of the bar are first discretized using the finite difference method, resulting in a set of ordinary differential equations that establish a state-space representation for the system. The high order of the resulting state-space model leads to a complex final controller, so reduced-order transfer function parameters are determined for different conductivity values using an optimization-based approach. Open-loop simulation results show that the obtained low-order models achieve over 99% accuracy for various conductivity cases. Internal model controllers are then designed for different conductivity scenarios using these reduced-order models and applied to the original system. Simulation results indicate that the designed internal model controller exhibits enhanced performance in tracking the desired reference input and rejecting disturbances compared to other methods. The system output effectively follows the desired temperature profile with appropriate speed, minimal overshoot, and zero steady-state error.