I don't understand how the machine captures the heat energy inside of it. If it is using natural gas it would not generate that much heat regardless. It is misleading to say that it is powered by heat.
Stirling engines are powered from a heat differential. If you put the whole machine in the fire, so to speak, nothing happens. But if you can heat one end of the machine while keeping "cooler" the other side, then you can generate power.
Stirling engines are sealed. Heat is applied externally. Natural gas, when burned, makes
great heat source.
More details:
http://en.wikipedia.org/wiki/Stirling_engine