This being the halfbakery, I'm ignoring the question of how to actually manufacture this desktop distraction.
Start with a clear glass torus, with an overall diameter of about 8 inches, with a tube size of about an inch.
Inside this torus, we attach several dozen semicircles of some nonporous material
(glass, metal, or plastic will work; other materials will also work). These disks alternate between being on the inner edge and outer edge of the torus, and are equally spaced around the torus.
The torus is filled with colored methylene chloride, the same liquid as is used in bubble lights and drinking birds. Half of the fluid (by volume) is liquid, and half is vapor.
The torus is mounted on a bearing, so it can spin freely on it's axis, with that axis being horizontal.
A lamp (which acts as a heat source) is placed below the torus, slightly to one side of the bottommost point.
The lamp causes the dichloromethane nearest to it to boil. The bubbles rise, but not directly to the top of the torus; they fill one of the gaps between a pair of adjacent semicircles mounted on the inner edge of the torus.
Since the lamp is off-center, the bubble trapped in the waterwheel is off-center. The buoyancy of the bubble pushes up on the disk, turning the torus, and moving the next gap closer to the lamp. As bubble after bubble forms, the wheel keeps turning.
Of course, the liquid displaced by the boiling liquid has to go somewhere -- it moves away from each newly formed bubble, and compresses all of the other gaseous methylene chloride elsewhere in the torus. This increases the temperature of that other dichloromethane, raising it to above the temperature of the air outside the torus. Naturally, the compressed gas cools, which causes it to condense.
The gas which is in contact with the coolest glass cools first/fastest, and the coolest glass is that which has been close to the lamp least recently... this glass is on the part of the torus which is at the top, or descending.
Naturally, this condensate will fall into one of the gaps between a pair of adjacent half-disks, and (due to gravity) pushes down on the lower disk, helping spin the torus.
As any particular disk that's holding liquid changes direction enough, that the liquid spills out. The continuous spilling of liquid makes this desktop toy resemble a waterwheel, and hence the idea's name.