If your pond water is only 1 degree, you are going to need circulating water at minus 3 to get any real pick up and preferably minus 5-6 .
Heat transfer is grossly affected by heat gradient.
Interesting facts.
I think it would be very interesting to drop a thermometer in our pond, fed by lands drains, and see what the temps look like through a winter at the base depth. Experience is that even in very cold weather, the water remains fluid and moving under a thin layer of top ice....