One option for the long-term disposition of excess weapons plutonium involves vitrification, which entails combining the plutonium with radioactive high-level wastes and glass frit in a melter and then filling small stainless steel "cans" with the molten mixture. Several of these cans are then placed on a "rack" within larger stainless steel canisters, which are subsequently filled with molten high-level waste glass (HLWG) for security against theft. This disposition alternative is referred to as the "Can-in-Canister" option [1]. Of particular concern is the ability of the molten HLWG to flow around the Pu-cans and their support structure to form a proliferation barrier. The canister filling process is investigated experimentally using room temperature model fluids as well as molten HLWG surrogates. Also, analytical results obtained from thermal models and detailed simulations show the role of heat transfer on the temperature distribution within the HLWG, and consequently on the strongly temperature dependent viscosity of the HLWG and its ability to flow and fill the canister.