A heat pump moves heat from one pool to another and adds whatever input energy required to move the heat to the whole system.
When you have two pools at different temperatures you can harvest energy from that difference but only as much as is there because harvesting the energy involves bringing the two pools closer in temperature.
There is nothing you can do to cheat this, whatever you do will bring the two pools closer together. If you bring in outside energy you will always be able to harvest less than you brought in.
No.
A heat pump moves heat from one pool to another and adds whatever input energy required to move the heat to the whole system.
When you have two pools at different temperatures you can harvest energy from that difference but only as much as is there because harvesting the energy involves bringing the two pools closer in temperature.
There is nothing you can do to cheat this, whatever you do will bring the two pools closer together. If you bring in outside energy you will always be able to harvest less than you brought in.