All of the pictures on this page are of an Ericsson Hot Air Engine, the last being a diagram of the engine innards. The Ericsson engine is a Stirling Engine meaning it does not burn fuel to operate.
It works using the energy from hot air. The engine has a hot side and a cold side. As the air trapped within the hot side heats it expands forcing the piston down. The hot air then forces its way into the cold side where it chills and contracts causing a vacuum in the hot side, the piston is sucked back up. The air then expands again causing the cycle to repeat. This is a terrible explanation of how these work - I'll have to update it one day.
In this case the air is heated by burning wood in a grate, it would work equally well with a gas burner, or a natural heat source such as a hot water spring (geothermic). There is a more info on Stirling Engines.
This engine is a pumping engine and manages a respectable 10 litres per minute even though the flywheel only turns at about 5RPM. Most of this engine was found by the side of a river where it had lain for years. Someone had stripped most of the brass from it (probably during World War 2 where such metals were at a premium). The owner (who did not want to be named) has machined the pump components by hand from stock brass and managed to gather parts to replace the missing bits. The engine is totally silent and will run as long as its heat source lasts.