This study investigates the dynamics and control of discretely heat integrated distillation columns, focusing on two configurations: one utilizing a liquid pumparound loop and the other employing liquid injection for waste heat recovery in a multi-stage vapor recompression cycle. These innovative designs eliminate the need for vapor splitters, simplifying operation and enhancing control robustness. As case study, the methanol/water separation process was modelled to achieve 99.99 mol % purity for both products. Dynamic simulations were conducted in Aspen Dynamics to evaluate the control performance for ± 20 % throughput and composition disturbances. Results demonstrated that the proposed control structures, which rely on inferential temperature-based strategies, effectively maintain product specifications and ensure stable operation. This work provides valuable insights into the practical implementation of discretely heat integrated distillation columns, offering a pathway toward energy-efficient and operationally flexible distillation systems.