This study presents a three-dimensional numerical simulation of chilled water flow in copper pipes installed on an aluminum plate using ANSYS Fluent to optimize the thermal performance of radiant ceiling panels. Unlike previous studies that have examined design parameters in isolation, the present work simultaneously investigates the coupled effects of four key variables pipe spacing, pipe diameter, mass flow rate, and inlet fluid temperature on cooling capacity and surface temperature uniformity. The flow was modeled as turbulent, incompressible, and transient, and the numerical model was validated against ASHRAE experimental data. The results show that reducing tube spacing from 0.30 m to 0.05 m increases cooling capacity by up to 35%; a practical range of 10–15 cm (60–63 W) is recommended. Reducing pipe diameter from 20 mm to 10 mm yields an 8% performance gain, with 12 mm (102 W) identified as the practical optimum. Increasing mass flow rate raises cooling capacity by 25%, with a pronounced step increase at the laminar-to-turbulent transition (0.016–0.017 kg/s). Inlet temperature exerts the largest influence, with capacity ranging from 108 W at 12 °C to 46 W at 18 °C; 15 °C is recommended as the optimal operating point. Transient analysis confirms that the panel reaches thermal steady state within approximately 3 minutes significantly faster than concrete-embedded alternatives. The coupled parametric framework provides a systematic basis for the component-level design of energy-efficient radiant cooling systems, advancing beyond prior single-parameter studies by quantifying the interactions among geometric, hydraulic, and thermal design variables within a unified model.