I have no insider knowledge of Google or Nest's plans. That said, the way they think about advertising isn't going to be about plastering ads on any surface with a screen. Instead, they want to use all sorts of sensors to learn more about you: when you're home, when you're away, etc., and feed you ads that are contextually relevant when you're somewhere that ads are acceptable (e.g., watching YouTube, doing web searches, running an app with banner ads).

That leads to the question of what they can learn from your thermostat & fire alarm that they can't learn from your phone and computer. I suspect the answer is "not very much yet" but Google is definitely keen to be a player in the "Internet of things" and Nest is a big player in that space. At the point where every light bulb, every electrical socket, every home appliance is connected to your home network, Google wants to be there. "Gosh, your dishwasher says the JetDry reservoir is empty. Buy more, click here!"