> Second, many coffee urns contain heating elements and thermostats, so as you take more coffee out of them, they actually perform a bit less work. There’s just less coffee left to keep warm.

I know this is just an analogy... but I don't think that's how heat transfer works. Heat loss here is primarily a function of temperature difference across the urn walls, and and thermal conductivity of the urn walls. I don't see how replacing coffee with air would slow down the heat loss.