It's possible to build a house that doesn't need any source of heat besides the sun and the warm bodies inside. Even in frigid Vermont.
Barbara and Steven Landau are building a house in Vermont—a handsome, three-bedroom, timber-framed 2,000-square-foot house—with neither a furnace nor any heat source. Again, this is in Vermont, where winters are long, dark, and frigid. The New York Times has their story, and this great video of the Landau's house under construction.
Be sure to also check out the Times' great graphic about the mechanics of a passive house.
Obviously, it's wildly frustrating that this style of "passive house" is possible—even becoming commonplace in Europe—but remains a complete anomaly here. (There are only 13 certified "passive houses" in the States.) Without broader recognition and a bigger market for the beefy insulated panels, the cost premium to build a passive house here in the States is pretty severe. In Europe it may add 2 to 3 percent to the final cost of building a house; here it's between 10 and 15 percent more expensive.
On top of that, the rest of the "conventional" home ownership industry is similarly lagging behind what's possible in engineering. The Landaus actually had loads of trouble finding insurance for a house in Vermont with no furnace. All the insurance companies told them their pipes would freeze, which is pretty absurd given that engineers advised the family against installing a fireplace, as it would make the house way too hot.