OK it wont be a "pure" mechanical solution, so wont rely only on the expansion of heat and the physics of a flywheel, but you could get better efficiency by loosing less to friction, and its probably a more silent, more practical and better for Low Temperature Difference (LTD), heres how: (halfbakery
oath inserted...)
There is only one NON-METALLIC canister filled with air, and well insulated from the heat.
In the middle of this cannister there is a "piston / displacer" that has a magnet attached to it. This piston divides the canister in two. The piston (with its magnet) is the only moving part. The magnet is used for energy output, as soon explained.
There are two winding radiators on each side of the cannister - possibly inside the cannister or connected to it so that the energy dissipates to the air in the cannister. So each side has one radiator for hot fluid and one for cold. These are used for the energy input.
The flow of hot or cold is controlled digitally, and is set to heat one side of the cannister while cooling the other, then changing the direction, heating the second side of the cannister and cooling the first.
The fluid is pumped (the only energy input besides the digital control unit) from the hotter and colder energy sources (such as a burning candle and an ice cube for a youtube demo or from the roof of a house and the front lawn, for a practical use).
The moving magnet can allow the heat energy to be retieved: Here are two examples how:
a. The magnet can pull or push a flywheel via a magnetic clutch (or magnetic gear - see links). This flywheel stores the energy or converts it to other forms of energy.
b. Or the magnet could press against another magnet, which by being repelled, compresses air.
For a large enough contraption it could work extremely slowly, giving high "torque".
Several of these units can be set in a circle creating a "rotary motor"
This type of motor could be set to receive large amounts of energy in a very small difference of temperatures ie from a solar heater on the roof and a cooler pipe in the lawn, or as another example: from along the dark and hot roadside (which is hot even at night as anyone who used a thermal [[NVD]] can attest to).
The "piston" could be set on a hinge in a u-shaped tube. If developed with high precision, it could confine the friction only to the hinge.
The cannister (and perhaps piston too) could be built to be very wide and thin so that minimal movement is done between cycles and a higher frequency achieved.
The whole thing wouldn't be all that efficient as a Stirling engine, but could be made mostly of plastic parts, real cheap and fast to apply, for solar power waste energy retrieval.