I soon realized...steampunk was the way to go.Link (Thanks, Brian!)
> Thus was born the Telecalculograph.
Not including the original PC, this project cost about $70 total. It took around two months of spare time, and was done with basic hand tools. The only power tools used were a drill and a Dremel.
Be sure to watch the video of the furnace in action here. *Note: The color of the "fire" is a little off in the video, in real life it is a more homogenous orange.