How about an electric blanket?

I would have hoped to store the bike outside so that I don't need to bring it inside. Hence the requirement that there be some sort of enveloping shell so that the generate heat stays inside.

A blanket would also get dirty pretty quickly with the dirty snow picked up from outside.

unless your bike has some areas that might catch water, then freeze (which I doubt), I can think of no reason why it can't be outside in any temperature. Neither steel or aluminum frames embrittle at anything near atmospheric temperatures and the tires and cables should be fine too.

That being said, when I lived in a dorm, I did keep my bike in my room, because it's just much nicer to get on a warm, dry bike than it is scraping ice off of the handlebars and lock. And yes, I've ridden at that temperature. Not fun, though.

bike lockers are sold, but I've never seen one.

http://www.bikeparking.com/btwlockerp/index.html

The blanket itself would tend to hold in the heat. You could put a tarp over it too, to help keep it dry and retain more heat. If you're only using it for your bike, who cares if it gets a little dirty? Really, I was kind of thinking of a purpose built bike blanket rather than a ordinary electric blanket. It could have a water-proof tarp-like outer covering sewn to it. It could also have zippers to close it on the ends.

A box would no doubt work though, as you suggested. However, a blanket has the advantage that you can fold it up and put it away when you don't need it.

BTW, I gave your idea a thumb up to help compensate for the two thumbs down other people gave you. I don't know why people gave you thumbs down. This isn't a bad idea.

I just have to ask why a bike needs to be kept warm? My car, which is a far more complicated piece of machinery, sits outside year-round with few ill effects.

A tarp over the bike to keep ice off the controls & seat would be enough.

Maby a better idea than heating the bike is to keep out the cold, i mean isnt that what ****bucks uses(im not going to use the real name because of copyright laws) to their coffee? Keeps the coffee hot while keeping the cold out.