A novel hot embossing process was used to construct a dense carbon fiber powder (CFP) network in the polydimethylsiloxane (PDMS) matrix of the PDMS/CFP composite, which was investigated experimentally. The results demonstrated that the addition of the filler and the decrease in sample thickness resulted in a significant increase in the thermal conductivity (TC) of the PDMS composites. TC of up to 19.325 W/(mK), which is as high as that of stainless steel (1Cr18Ni9Ti), was achieved at a filler content of 60 wt% and a thickness of 0.2 mm. A mathematical model for predicting TC was established, and the filler content, compression coefficient, and interfacial thermal resistance were systematically discussed. In addition, finite element analyses were performed to predict the TC of the PDMS/CFP composites with various thicknesses and filler contents. The numerical and theoretical results were in agreement with the experimental results. Finally, the PDMS composite was tested as a heat spreader, which significantly reduced the temperature.