The goal of the personal stirling engine is to provide onsite power generation for a location (like a house).
The personal stirling engine consists of a Displacer-type Stirling Engine that is half above ground and half below ground. The theory being that in the summer it is warmer above ground and cooler below ground. In the winter it would be cooler above ground and warmer below ground. Your climate may vary.
The difference in heat causes a difference in pressure of the gas sealed inside the engine. The difference in pressure causes the piston to move up and down. The piston movement turns a turbine which generates power.
Looking around the internet at various existing technologies I've come across some numbers which would have to be met in order to make this viable. They may or may not be reliable but are listed below:
1200 degrees F can generate 5KW. Alternately -1200 F could generate the same 5KW?
Multiple stirling engines uses in tandem (2 or 4) work better than a single one?
Most of the things mentioned below wouldn't produce enough heat/cold to be effective.
The two most promising solutions seem to be using solar energy or liquid nitrogen.
Example:
There are various ways to enhance the temperature both above and below ground.
Above Ground:
Mirrors directing sun at the engine cylinder. There are actual test units called dish/Stirlings? which do this already. Roughly, a 18 foot diameter mirror will generate 5KW. They concentrate about 1200 degrees F of heat on a stirling to run it.
Solar oven with the engine cylinder at the center.
Insulation.
Engine cylinder covered in a material that retains and radiates heat.
Painting the engine cylinder black so it absorbs more heat.
Attach a wind turbine to the top of the Stirling Engine to provide extra electricity or provide extra heat/cool for both ends.
Attach a solar panel to the Stirling Engine to provide extra electricity for either cooling or heating of each end.
Attach heat sinks (ala a CPU?) to the Stirling Engine chamber.
Electric heating coils.
Encase one end of the Stirling Engine chamber in the water heater for the location.
Below Ground:
Generate liquid nitrogen(-200 celcius) onsite and use it to cool the stirling engine. There are current liquid nitrogen generators that can generate up to 90L an hour. There are current liquid nitrogen containers that only lose .14L/h of liquid nitrogen.
The engine cylinder in a tank of cool liquid (water?).
The engine cylinder in a tank of anti-freeze.
The engine cylinder in a refrigerated unit (powered by the engine).
The engine cylinder surrounded by rotting compost (which generates heat).
A deep sunk pole to bring heat up from farther down in the crust to the engine cylinder.
Use the material that absorbs heat on one frequency and releases it on another frequency as insulation.
There are various ways to enhance the temperature both above and below ground.
