A process for insulating the void in a thermal distance piece in a low-temperature or cryogenic storage tank uses a vacuum source to draw insulation into the TDP. Two remotely spaced openings to the void are provided. A strainer is temporarily mounted in one of the openings. The other opening is connected to a suction wand. The wand has an inner cylinder that extends through an outer cylinder and projects outwardly from a proximal end of the outer cylinder. Distal air vents are provided on the inner cylinder, near a distal cap that connects distal ends of the cylinders. Proximal air vents are provided on a proximal cap that connects a portion of the inner cylinder to a proximal end of the outer cylinder. The distal end of the wand is inserted into a container of insulation.