Pipe-embedded walls offer a promising approach to reducing winter heating demand by mitigating envelope heat loss while maintaining indoor thermal comfort. However, most existing studies focus on single-pipe systems operating under high-flow conditions, with limited attention to low-flow operation and its implications for energy flexibility. This study investigates a parallel pipe-embedded wall system operating at low flow velocity as a flexible heating strategy. A three-dimensional CFD model was developed to analyze the coupled hydraulic and thermal behavior of the wall, including the effects of connecting columns, and was validated through experiments under identical boundary conditions. Parametric analyses examined the influence of main pipe size, branch spacing, flow velocity, water temperature, and column-induced thermal bridging. The results show that variations in flow velocity and branch spacing lead to flow distribution differences of up to 6%, while causing negligible changes in inner-surface temperature (below 0.1 °C). In contrast, increasing column size significantly intensifies thermal bridging, increasing inner-surface heat flux by approximately 21% as the column edge length increases from 200 mm to 400 mm. Overall, the results demonstrate that parallel pipe-embedded walls can enhance building energy flexibility by enabling stable thermal performance under low-flow operation.