Cover it with an insulated top when not in use. Your pool is colder than ambient because the top surface is constantly evaporating, leaving behind the slower moving molecules.

A solar heater would work better (if you have sun) because it will absorb more energy than ambiant air convected over the same area. And you would need a fan for a heatsink if its wasn't windy. http://www.amazon.com/SmartPool-SunHeater-Above-Ground-Pools...

A way for you to test it would be to do it on a small scale - maybe buy some copper tube and circulate an aquarium with the water filter pump.