Insulate your home properly, set it to a constant, comfortable temperature, and you're done. You'll save FAR more money, the entire family and all your pets will be FAR more comfortable (oo, need to pad off to the bathroom at 2 am? Too bad it's 50 bloody degrees, eh?)
Seriously people, wake up and smell the coffee. You're paying to heat and cool the outdoors. Stop doing that. Best investment you can make in bill reduction, and unlike a thermostat that plays freeze-your-toes-at-night, the investment will pay you back the entire time you own your home.
Start by buying a cheap thermal sensor gun, plug all the little holes and leaks. There will be plenty. Then call an insulation company and see what they can offer you. Your wallet will thank you. So will your bare feet. And you can put your sweaters away.
Oh yeah... new construction? Contract for thicker, better insulated walls. Go overboard. It's not even that costly. Your power and gas companies will hate you for it.