Lightweight and elastically deformable soft materials that are thermally conductive are critical for emerging applications in wearable computing, soft robotics, and thermoregulatory garments. To overcome the fundamental heat transport limitations in soft materials, room temperature liquid metal (LM) has been dispersed in elastomer that results in soft and deformable materials with unprecedented thermal conductivity. However, the high density of LMs (>6 g cm⁻³) and the typically high loading (⩾85 wt%) required to achieve the desired properties contribute to the high density of these elastomer composites, which can be problematic for large-area, weight-sensitive applications. Here, the relationship between the properties of the LM filler and elastomer composite is systematically studied. Experiments reveal that a multiphase LM inclusion with a low-density phase can achieve independent control of the density and thermal conductivity of the elastomer composite. Quantitative design maps of composite density and thermal conductivity are constructed to rationally guide the selection of filler properties and material composition. This new multiphase material architecture provides a method to fine-tune material composition to independently control material and functional properties of soft materials for large-area and weight-sensitive applications.