Stirling Engines and Heat Pumps

Just read this post. In the comments there is a link to Heat Pumps & some talk about their use.

My comment was...

Why would you get a headache?

You have a heat to motion to electric power system, where part of the electric output is feed back into the system to improve efficiency and/or decrease the cost of the total system.

How is this so. Well if you use the heat pump to 'focus' the heat into a 'point' of higher temperature, you can do two things. Increase its efficiency (by changing the hot-end temperature & thus the hot-end cool-end ratios, as measures in degree K). You can also use the smaller & cheaper (per unit of energy output) stirling engine.

Anyway, that how I read it. Comment welcomed!