I don't think it would last very long on batteries
That's exactly what I thought. I didn't think it would be possible for it to run for any longer than 3 days at best. However, I did some Googling and found this page which has a simple setup of an Atmega 168 connected directly to 3 batteries, running a small program which puts the chip to 'sleep'. By using just the Atmega means power is not lost on the onboard USB chip and the voltage regulator, as in a normal Arduino! Looks like a pretty sweet solution and can last for 3 years. I have no experience with dealing with loose ATmega chips and loading them with programs, etc...
http://interface.khm.de/index.php/lab/experiments/sleep_watchdog_battery/
But I'm questioning why you're placing the thermostat near the furnace anyway, how come you can't place it in your main living area?
I could put everything in one box in the living area (like you have) but the problem is that my boiler is in the kitchen, a couple of rooms away. In order to control my boiler I'd have to put wires in the walls (=trouble) or use a wireless link (yay!). If I'm using a wireless link I thought I might as well also make the thermostat enclosure itself portable so that it isn't limited to one room. It could be in the bedroom at night and then go to the living room in the day. Hope that makes sense. It might just be a bad idea!