The moving carbon nanotube heat sink includes a heat transfer belt comprised of highly thermally efficient carbon nanotubes. Laterally disposed cooling fins extend away from a top surface of the belt. The belt is slidingly disposed over a C-shaped channel made of metal or other suitable material that is mechanically and/or chemically connected to a top surface of an electronic chip. Belt movement may be powered and guided by a plurality of rollers. The cooling occurs primarily as a result of conduction and convection heat transfer modes.