An effective battery thermal management system (BTMS) for electric vehicles is imperative to enhance energy density while ensuring efficient thermal control in a compact, lightweight design. The previous works focused on reducing the maximum temperature and temperature non-uniformity in the battery pack while weight-ratio of the BTMS is given less attention. This study introduces a liquid-cooled BTMS with heat-conducting elements (HCEs) featuring three curved surfaces and a central liquid coolant path. These strategically placed HCEs form a compact structure within the battery pack, addressing the critical need for weight reduction in the BTMS. The research investigates the impact of variable parameters, specifically the surface contact angle (Δα) and height (Δh) of HCEs along the flow direction. Numerical analysis reveals that designs incorporating HCEs with variable contact areas outperform those with constant contact areas. Among the twenty designs considered, HCE-3e, with a contact angle (Δα) of 10° and a height (Δh) of 5 mm, emerges as the optimal solution. This design demonstrates a remarkable 75.63 % reduction in temperature non-uniformity (ΔT) and a 41.8 % reduction in HCE weight compared to the base design (HCE-0a). Importantly, the proposed BTMS design with HCE-3e constitutes only 6.3 wt% and 9.2 vol% of the battery pack, significantly reducing the system's weight and volume compared to prior studies. In addition to structural improvements, the study explores the use of copper–water nanofluids to enhance thermal performance. A nanofluid with 7.5 vol% of copper exhibits superior heat transfer efficiency, achieving a 4 % reduction in maximum temperature (Tmax) compared to pure water. Furthermore, this nanofluid requires a 20 % lower volumetric flow rate than water to maintain Tmax below 35 °C, with an equivalent pressure drop of 280 Pa. The proposed BTMS design (HCE-3e) coupled with nanofluids offers a practical and efficient solution for the thermal management of cylindrical lithium-ion batteries. This integrated approach improves heat transfer efficiency and reduces the demand for high pumping power, enhancing the system's overall effectiveness.