This might move you out of your comfort zone, but there is/was an initiative called LowEx that tried "Low Exergy" heating and cooling.
Here's a link to one of their reports:
https://www1.ethz.ch/gt.arch/news/Lo...atPump_Meggers
and the following diagram is in it:
Moral of the story: "The Lower the lift, the greater the COP"
Although it's not stated, to work with LowEx, Heat Exchangers need to be very efficient because the delta-T is low. So, all the many techniques that would raise the efficiency of a HX, like larger than usual area and higher than usual fluid velocities would need to be employed.
-AC