An apparatus includes a substrate having a recess and a first insulator submerged in the recess of the substrate. The apparatus also includes a cover having a second insulator that, together with the first insulator, defines an insulated volume. The apparatus further includes one or more components to be cooled located over the first insulator and within the insulated volume. The apparatus could also include one or more electrical conductors located over the first insulator, where at least one of the one or more components is electrically connected to the one or more electrical conductors. The one or more electrical conductors could be submerged in the recess of the substrate. The one or more electrical conductors could be thermally-insulative at cryogenic temperatures and could include carbon nanotubes. The first and second insulators could include foam or aerogel insulation.