Effective thermal management has become an essential part of the machining process, as the excessive temperature generated detrimentally affects tool life, dimensional accuracy, and the metallurgical properties of both the tool and the workpiece. With the advancement to Industry 4.0, the design of multifunctional materials has become one of the key focuses of advanced engineering. This study numerically presents an essential first step of designing a multifunctional cutting insert to obtain effective heat dissipation from the cutting tool tip by incorporating copper as a conductive material within cutting inserts, along with the thermal impact of the conductive material’s geometry, placement, and size. Findings demonstrated that the overall integration of conductive material significantly reduces the tool tip as well as the overall body temperatures. Among all the tested geometries of conductive material—circular, rectangular, square, and trapezoidal—the trapezoidal shape exhibited the most effective performance in lowering cutting temperature. The placement of conductive material near the tool tip and rake face proved to be highly efficient, while positioning beyond the heat-affected zone had negligible influence. Additionally, the effect of coolant velocity was found to be marginal after the introduction of conductive material, with a temperature reduction of less than 40 K between 1 m/s and 10 m/s. The most notable result was achieved with trapezoidal copper inserts, where a temperature drop of 478.89 K was observed under optimized conditions. Overall, this study establishes conductive material incorporation as a promising strategy for enhancing heat dissipation and minimizing thermal issues in metal cutting. While the findings of the foundational thermal analysis of the multifunctional W-Cu insert made it persuasive, it concurrently drew the mechanical challenges of structural integrity.