Still can’t picture it? Try this: A solar-powered furnace is a slab of coated metal and a fan. The technology, which was patented way back in 1881, Mr. Edens said, operates when the sun shines.

But let’s get back to that cold winter a dozen years ago in Pine River, Minn. Mr. Edens, then a graduate student in environmental policy, was so poor that he ran out of propane to heat his 1,250-square-foot home.

Like some seven million American households, he said, he received a break from the Low Income Home Energy Assistance Program, a $3-billion-a-year (and shrinking) federal block grant. (This year, program data suggest, New York will shovel almost $340 million into helping households pay heating and air-conditioning bills. While “fuel poverty” is persistent and pernicious, Mr. Edens said, “instead of applying a solution, we’re just hemorrhaging money.”) That was when he heard about a home changing hands in St. Paul that had a solar thermal system, he said — that is, a solar-powered furnace.

“They were discarding it, but it was fully functional,” he said. “I drove down to St. Paul in a pickup truck and literally went Dumpster diving. I installed it on my house. We saved so much money, I had a moment where I said, if we can save this money in Minnesota. ...”

And now the fine print. A completely installed solar furnace system typically costs $5,000 to $7,000, before any renewable energy tax breaks and rebates. (These incentives often add up to about 50 percent of the total costs.) Still, with natural gas prices at frack-tastic lows, a solar-powered furnace remains a long game.

The panels, which measure 24 to 40 square feet, lie vertically against the south side of the house to capture rays from the low winter sun. (The system typically doesn’t need to run at all in the summer; remember, it’s not making electricity.) This positioning means that trees and other buildings in a city landscape will easily shade them out.

Taking these two factors together, Mr. Eden has devoted most of his organization’s attention to open, rural areas, where many homes rely for heat on pricey propane and heating oil. (The average Northeastern household that heats with these delivered fuels spent more than $2,300 last winter, according to Energy Department data. That new solar thermal system doesn’t seem quite so dear by comparison.)