One does not need to take a journey to the center of the Earth to get this energy. At about 30 feet into the Earths surface the temperature stays relatively constant. Geothermal heat pumps work by carrying heat from one place to another. In warm locations such as tropical islands heat pumps can transfer heat from the home down into the ground thus cooling the environment much like a refrigerator. In cold locations such as northern islands, heat pumps can transfer heat from the ground into a building. Thus through this simple system you can produce ambient air that warms or cools your home depending on the location of your island.
The process of instillation is also relatively straightforward. A big coil of plastic pipe is attached to the dwelling at one end and buried into the ground at the other. The pipe is filled with a liquid that is an excellent conductor of heat. The liquid takes heat from the ground and carries it into the building. Another set of pipes within the building also has liquid in it. This liquid picks up the heat coming from the pipe outside (think of it as a relay race). The pipe in the building carries the heat to an appliance that will warm up air or water. In tropical locations the cycle is reversed. The more heat or cooling you need determines how deep the pipe needs to go into the ground.
Geothermal power can be expensive with costs ranging from $14,000 to $25,000. Nonetheless the system is low maintenance and completely renewable with the system typically paying for itself in about 7 to 10 years. Geothermal heat pumps are ideal in a variety of climates, the only restriction is the system requires a large area to lay down the pipes. Therefore if your island is small it may not be big enough to accommodate a geothermal heat pump.