This study investigates the thermal performance of a parallel-flow double-pipe heat exchanger using three different inner-tube geometries—circular, circular-cut, and rectangular-cut—to evaluate how geometric modifications enhance heat transfer in systems with naturally limited thermal gradients. Computational Fluid Dynamics (CFD) simulations were carried out in ANSYS Fluent under steady-state, laminar flow conditions using water as the working fluid, with a 250 mm exchanger modeled to capture conjugate heat transfer and temperature distribution for each geometry. High-quality meshing, boundary-layer refinement, and accurate inlet temperature settings enabled detailed analysis of thermal behaviour across the inner and outer flow regions. The results show that modified geometries significantly improve fluid mixing and boundary-layer disruption, leading to enhanced convective heat transfer compared to the standard circular tube. The circular tube produced cold- and hot-outlet temperatures of 306.30 K and 338.46 K, while the circular-cut tube improved performance with outlet values of 306.19 K (cold) and 331.20 K (hot). The rectangular-cut tube achieved the highest thermal enhancement, raising the cold-fluid outlet temperature to 307.41 K and cooling the hot fluid to 336.81 K, demonstrating that geometric optimization—especially the rectangular-cut design—substantially strengthens heat-transfer effectiveness in parallel-flow heat exchangers.