data furnace
n. A computer installed in a home or office to be used as both a server and the building's primary heat source.
Examples
2011
Instead of fighting the heat they want to create data furnaces which will use the heat to heat homes and businesses. Their idea is to sell fully enclosed data furnaces much like a regular furnace. The data furnace would physically fit into a basement or closet and integrate into an existing duct system to distribute heat. Additionally, the data furnace would be connected to the Internet and be secured from tampering.
—Russell Hitchcock, “Data Furnaces,” Windows Networking, September 08, 2011
2011
Then, there's this: Microsoft research suggests the possibility of "data furnaces," small server packages of consisting of tens or hundreds of processors engineered to plug into existing HVAC systems to contribute their excess thermal energy to the heating of air and water in the home.
2011 (earliest)
In this paper, we argue that servers can be sent to homes and office buildings and used as a primary heat source. We call this approach the Data Furnace or DF.
—Jie Liu, et al., “The Data Furnace: Heating Up with Cloud Computing” (PDF), Microsoft Research, July 25, 2011
Notes
What may make sense in the future is something that has been referred to as a "data furnace."

The data furnace is a powerful computer that serves the same function in a home as a mainframe or minicomputer in a company's local area network, providing centralized processing power to perform entertainment and PC computing functions.
—Gerry Blackwell, “The PC: your next entertainment centre?,” The Toronto Star, December 11, 1997