[Leonard_of_Q]

That is what you use the heat pumps for, to transform what you call "low-grade heat" to... "higher-grade heat"?

The COP for a heat pump doing such a transformation can be very high, i.e. for a relatively low power input you get a lot of gain.

[mlyle]

Do the math on pumping 40C water any distance in a loop. It is hard to make it worth it. The water cools off and the pumping takes significant energy, plus the pump and all the piping cost something.

Then using a heat pump on it makes it even worse.

Low grade heat source is not a term I made up- it refers to heat sources under 100C.

Even much hotter low grade heat usually goes unused. You usually need a perfect confluence of a warmer source, very close need for building heat, and a willingness to pay more for environmental friendliness for it all to work out.