That's not how entropy works. The heat already goes inside and is hotter than the hot side so your heat pump would just waste work. You /could/ use a heat engi

That's not how entropy works. The heat already goes inside and is hotter than the hot side so your heat pump would just waste work. You /could/ use a heat engine to diffuse your high grade heat and use the work in your heat pump. But that would require more moving pieces (or a complicated heat engine in your heat pump that could extract work)