Compact plate-fin intercoolers are widely used in natural gas compression stations; however, previous studies typically analyze isolated parameters, assume constant thermo-physical properties, or neglect the combined thermo-hydraulic impact of nanofluids under realistic operating conditions. This study presents a detailed numerical investigation of the thermo-hydraulic performance of a compact plate-fin intercooler evaluated for a natural gas compression station, explicitly addressing this gap through an integrated parametric framework. A model was implemented in Engineering Equation Solver using temperature-dependent thermo-physical properties for natural gas and the coolant, including copper oxide–water nanofluids. The effects of the gas Reynolds number (4000–12000), the imposed coolant-side temperature difference (8–12 °C), and the nanoparticle volume concentration (0–0.5%) were systematically evaluated in terms of overall heat transfer coefficient, required heat exchanger volume, and pressure drops on both sides. The results show that increasing the gas Reynolds number is the dominant enhancement mechanism, raising the overall heat transfer coefficient by approximately 35–40% and reducing the required volume by 30–45%, while increasing the gas-side pressure drop by 250–350%. However, the absolute magnitude of the gas-side pressure drop remains very small (approximately 2–18 Pa), representing a negligible fraction of the operating pressure of the compression system. Increasing the coolant temperature difference has a minor effect on the overall heat transfer coefficient (2–4%) but contributes to volume reduction with limited hydraulic impact. Nanofluids improve the overall heat transfer coefficient by 6–9% and reduce the required volume by up to 7–12%, although the coolant pressure drop increases due to higher effective viscosity. These findings provide a clearer thermo-hydraulic trade-off framework for compact intercooler design.