The demand for high-end performance coupled with the continuous miniaturization of electrical and electronic devices has resulted in a significant increase in heat flux generation. Metal matrix composites (MMCs) are frequently used as heat spreader materials in electronic devices due to their enhanced thermal conductivity, mechanical properties, and other key characteristics, addressing the challenges posed by increasing power density in electronic and thermal systems. This study focuses on testing copper silicon carbide (CuSiC), a metal matrix composite, as a heat spreader placed between a heat source and a heat sink. Copper, which is used in microcontrollers and microchips, serves as the heat source. To facilitate more efficient heat removal and transmission from traditional high-power-density chips, a thermal management technique involving thermal interface material (TIM) has been applied, using graphene-based paste as the TIM between the specimens. The thermal conductivity of CuSiC has been experimentally estimated with temperature using the ASTM D5470 method. Subsequently, the heat transfer between the copper and CuSiC contact has been evaluated experimentally in terms of Thermal Contact Conductance (TCC), an important performance parameter. Axial heat flow experiments were conducted using a simple and reliable experimental setup based on the steady-state methodology. Initially, experiments were performed on bare specimen contacts across a range of input heat flux (21–69 kW/m2) and contact pressure (0.1–0.4 MPa). The experiments were then repeated under similar conditions with graphene paste as the TIM between the specimens. The results indicate improved TCC with graphene paste compared to bare contacts. The findings of this study are applicable to thermal management applications in electronic devices.