The embodiments herein describe technologies of cryogenic digital systems with a first component located in a first cryogenic temperature domain and a second component located in a second cryogenic temperature domain that is lower in temperature than the first cryogenic temperature domain. An electrical conductor is coupled between the first component and the second component along a first plane. The electrical conductor carries a signal between the first component and the second component. A cooling assembly is coupled to a segment of the electrical conductor. The cooling assembly may include an electrical insulator including ceramic material. The cooling assembly may include a cold plate, two cold plates, or an orthogonal cold strip.