Dissimilar welding between copper (Cu) and stainless steel 316L (SS316L) is essential for heat pipe applications that require high thermal conductivity combined with adequate mechanical integrity. However, the large mismatch in thermal and metallurgical properties between Cu and SS316L complicates joint optimization. This study investigates the effect of heat input (HI) during TIG welding with an ERCuSi-A filler on the microstructure, mechanical behavior, and thermal conductivity of Cu/SS316L dissimilar joints. Three heat input levels (1.41, 2.02, and 2.04 kJ/mm) were applied under identical welding conditions. Microstructural evaluation was performed using optical microscopy and Scanning Electron Microscopy coupled with Energy-Dispersive X-ray Spectroscopy (SEM–EDS) to assess grain evolution, elemental diffusion, and weld metal homogeneity. Tensile testing showed that fractures consistently occurred in the Cu heat-affected zone, indicating that the Cu-rich weld metal was mechanically stronger than the copper base material. Increasing heat input promoted grain coarsening, SS-rich particle agglomeration, and microstructural heterogeneity. Thermal conductivity decreased after welding, with measured values of approximately 264, 198, and 111 W/m·K for heat inputs of 1.41, 2.02, and 2.04 kJ/mm, respectively, lying between those of Cu and SS316L. Overall, a low heat input of 1.41 kJ/mm provided the most favorable balance between mechanical integrity, microstructural stability, and thermal conductivity. These findings highlight the importance of precise heat input control when designing Cu/SS316L welded joints for heat pipe systems.