Closed-cell foams are widely applied as the material of choice for thermal insulation, which is essential for the thermal management of buildings, organisms, and many industrial processes. Foam insulation is often comprised of a polymeric matrix with dispersed, closed cells that are filled with an insulating gas. We develop and demonstrate a processing technique for replacing the typical fill gas with a variety of high-molecular-weight, superior insulating gases for significantly improved insulation. We focus on neoprene foam, which is a closed-cell synthetic rubber foam with a thermal conductivity of 0.050-0.060 W/m-K. With our processing technique, we achieve a thermal conductivity of as low as 0.031 W/m-K for neoprene foams, the lowest value that has been measured for neoprene foams to date. We show that this reduction in thermal conductivity can be accurately predicted by analytical models and numerical simulations. A simple Fickian diffusion model describes the processing technique and agrees well with experimental data. Finally, we demonstrate that similar reductions in thermal conductivity can be realized for neoprene in the form factor of a wetsuit using our simple charging procedure. Whereas conventional wetsuits allow divers to spend only 15-30 minutes in cold water (<10 °C) before they become vulnerable to hypothermia, the results in this work could enable divers to safely spend 2-3 hours in the water.