The heat gradient here is the big point. If you can use one kilowatt of power to pump 4 kilowatts of heat from one room to another, to turn some of that into el

The heat gradient here is the big point. If you can use one kilowatt of power to pump 4 kilowatts of heat from one room to another, to turn some of that into electricity you need to use the temperature gradient between the two rooms, and therefore let that heat flow back into the room you're cooling. If 400% is peak, and you get 50% efficiency out of the heat pump, you can do it at peak at 200% efficiency, but that's only at peak, and at full efficiency of the heat pump. Unfortunately, the higher the temperature gradient in the direction you're pumping, the less efficient a heat pump is, so you won't get anything near peak efficiency. Not at peak and/or with too low a temperature gradient and you can't do it, you'll be not cooling the room you're trying to cool at all and spending electricity to accomplish nothing.