Soft materials with high thermal conductivity are critical for flexible electronics, energy storage and transfer, and human‐interface devices and robotics. However, fundamental heat transport limitations in soft and deformable materials present significant challenges for achieving high thermal conductivity. Here, a systematic study of soft composites with solid, liquid, and solid–liquid multiphase metal fillers dispersed in elastomers reveals key strategies to tune the thermal‐mechanical response of soft materials. Experiments supported by thermodynamic and kinetic modeling demonstrate that multiphase systems quickly form intermetallics that solidify and degrade mechanical response with modest gains in thermal conductivity. In contrast, liquid metal inclusions provide benefits over solid and multiphase fillers as they can be loaded up to 80% by volume with the composites being electrically insulating, soft (<1 MPa modulus), and highly thermally conductive (k = 6.7 ± 0.1 W m−1 K−1). The thermal‐mechanical response of the composites is summarized and quantitative design maps are presented for soft, highly thermally conductive materials. This leads to soft materials with unique thermal‐mechanical combinations, highlighted by a liquid metal composite with an unprecedented thermal conductivity of 11.0 ± 0.5 W m−1 K−1 when strained. These materials and approach enable diverse applications from soft conformal materials for stretchable electronics to thermal interface materials in integrated circuits.