I have not run any significant numbers, but my gut feeling is that you will not be able to do any reasonable pond-area heating without a very substantial heat source.
Let's assume that Kenc's smaller 13 acre pond has an average depth of 6 feet. That is:
13 acres x 6 feet = 78 acre-feet
An acre-foot of water contains approximately 325,851 gallons.
78 acre-feet x 375,851 gallons per acre-foot = 25,416,378 gallons
It takes approximately 8.34 BTU to raise a gallon of water one degree Fahrenheit. It takes a little more, or a little less, depending on the actual temperature of the water, because BTUs are based on weight, not gallons. I'm assuming that a gallon of water weighs 8.34 pounds.
It then takes:
25,416,378 gallons x 8.34 BTU/Gallon/per F degree rise = 211,972,592 BTU to raise that pond just one degree F.
There are approximately 140,000 BTU per gallon of home heating oil.
Assuming 100% efficiency (which we cannot possibly achieve), it would take:
211,972,592 BTU per degree rise / 140,000 BTU per gallon = 1514 gallons of fuel oil needed to raise the water 1 degree F.
So let's say the pond is at 40 degrees, and we want to raise it to 60 degrees, so the fish will start feeding.
That would require over 3000 gallons of fuel oil just to get us to a feeding temperature. Then we would have to maintain that temperature for a period of time to be effective.
Now, granted, the pond will have thermocline layering, currents, and other factors. These will keep any small area from becoming significantly warmer or cooler than any other part of the pond at that same depth, but not substantially. The pond will also have evaporative cooling. This time of year, it may have inflow of cooler water.
In any case, it would take enormous amounts of energy to heat a small area of a pond to the point where warm water fish, like bluegill, crappie, and bass would become active feeders.
Without significant inflow of very warm water, such as from a power plant or office building, I believe that trying to warm a body of water this size, would be cost prohibitive to the average individual.
If this was for a cold water species, such as trout, moderate volumes of well water or spring water could affect a certain small area. I believe Cecil does this in his ponds, but they are much smaller.
In the continental US, well water from 20 feet below the earth's surface is roughly equal to the mean annual air temperature, at that latitude, at the surface. In most cases, well water will not exceed 60 F degrees in the continental US. Where Kenc and I live, water from 20 feet below the ground surface is typically in the mid-50 F degree range. It will stay at that temperature to extremely deep depths.
I would be happy to be proved very wrong -- and I'd go try it myself. But, I just don't see any economical and practical way to raise the temperature, even in small areas of a pond of this size.
In smaller ponds, it certainly could be possible to use solar heating, especially solar heating of an incoming water source, such as a well.
Heated cage culture maybe? But, then why not aquaponics or indoor fish raising?
