Presented are electrical conductor assemblies with vascular cooling systems, methods for making/using such assemblies, and vehicles equipped with such assemblies for transmitting power and coolant between electric devices. An electrical conductor assembly includes an outer sheath, an electrical conductor extending through the sheath, a coolant channel defined through the sheath, and an optional cable jacket encasing the electrical conductor. The outer sheath has a tubular body formed from an electrically insulating material. The electrical conductor has a solid cable body located within a conductor duct extending through the sheath. The coolant channel, which is coaxial with and thermally connected to the cable body, passes therethrough coolant fluid that cools the electrical conductor. The cable jacket may be formed from an electrically insulating material having a thermal conductivity and melting point higher than that of the sheath. The conductor assembly may include multiple electrical conductors circumferentially spaced around the coolant channel.