In reply to TobyA:
> the heat is radiating through all the material of the flask.
Heat radiates from the core of the flask whether or not there"s a vacuum...
Vacuum flasks insulate by preventing conduction to the surrounding air. Stainless flasks have a bit of a flaw in that steel is rather thermally conductive, so heat flows up the inner, to the neck, and then down the outside. Adding extra insulation will help. But if the vacuum has gone, the flask won't work well. But that's not because of radiation...
In a glass flask, glass isn't as conductive, doesn't come up to the neck/cap, and has a protective shell that is often insulated further.