I don't think that a 24/7 network connection of a customer that just paid $249 for a thermostat is that much of an monetization issue for a company like Google. (for comparison: more than 1 billion Android devices are currently connected to their servers 24/7/365)
Well in addition to the color LCD, they do have speakers so Google could do audio ads.
Also, Google+ checkins when you walk into your house and G+ status updates when you adjust your temperature would increase the G+ 'active user' count for them.
