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Glass is far inferior to paper, plastic and Styrofoam in terms of insulation. Thermal conductivity in terms of BTU/(feet - hour - degrees F) is 1.82 for glass, 0.09 for paper, 0.06 for Styrofoam. The conductivity of plastics varies depending on the materials: for polypropylene and polycarbonate, the thermal conductivity values are 0.69 and 0.35, respectively.
The plastic is polymer. Polymers can be thermal and electrical insulators. For example, pots and pans handles are made of polymers, so are insulated cups, coolers, and microwave cookware. Remember that styrofoam is a trademarked name of the Dow chemical company for its brand of polystrene foam. It works by reducing a process known as heat transfer.