Higher power densities and consumption in electronic devices require heat dissipating components with high thermal conductivity to prevent overheating and improve performance and reliability. Polymers offer the advantages of low cost and weight over metallic cases, but their intrinsic thermal conductivity is low. Previous studies have shown that the thermal conductivity in polymers can be enhanced by polymer chain alignment or by adding high thermal conductive fillers to create percolation paths inside the polymeric matrix. Typical thermally conductive polymers have moderate in plane conductivity, but low cross plane conductivity. Cross plane thermal conductivity is critical to removing heat from active devices and transmitting it to the external environment. In this study, we combine conductive fibers and fillers to enhance the thermal conductivity of polymers without inducing significant thermal anisotropy while maintaining the mechanical performance of the matrix. We fabricate our thermally conductive polymer-matrix composites by infiltrating Ultra High Molecular Weight Polyethylene (UHMW-PE) chopped fiber mats with a mixture of EGaIn liquid metal alloy and a thermoset polymer matrix. Subsequently, we characterized the thermal performance of the composites using infrared thermal microscopy with two different experimental setups, allowing us to independently obtain values for in-plane and cross-plane thermal conductivity. The results demonstrate that the network structure achieved by the fiber mat, in combination with the liquid metal, enables a uniform increase in the thermal conductivity of the composite in all directions. We also assessed the impact of filler concentration on matrix performance through indentation and tension testing.