Aliaksei Zholner from Belarus has built a functioning Stirling engine of paper that he demonstrates in a video. He has also published a construction description at a forum of the paper builders. The text is in Russian but translates nicely through Google Translate.
A Stirling engine operates on a closed cycle in which a working fluid is cyclically compressed and expanded at different temperatures.
This model is made of paper, it can run on a bowl of hot water and ice up to 13 minutes. Top and bottom surfaces of heat exchanger are made of office paper reinforced with cardboard ribs, most of parts are soaked with superglue to achieve strength and water resistance.
Displacer is also made of office paper, and its drive is made in the form of oscillating frame, as it is not possible to make it as a conventional airtight vertical rod. Diaphragm is made of napkin covered with glue for rubber.