Air cools very quickly and aquarium pumps don't have an inlet to bring air in from a warm room so they would have to be in a box like you said with some sort of heat form, so really you're running two things that require electricity to do one job. Even then the air would probably be water temp by the time it gets to the bottom anyway.
Unless you get a high powered pump you're not going to get much water movement, a cheap brand of either a filter pump for 60 gallons will move water pretty well, but run you about $30, at which price you can just buy a heated waterer or a tank heater for a stock tank ( $20) , a double air pump for a tank will run you about $20 or more as well, and I still don't think they'll move much water, this is coming from years of aquarium experience with everything from a 5 gallon to 80 gallons.
Heating elements really don't take a lot of heat, you can also get heat tape that is used to wrap water lines. Heating element doesn't take any more heat than say not turning off the computer, or even as much as most households use just having stuff they aren't using plugged in, such as stereos with displays, VCRs/ DVD players, tv's that have little lights that say they aren't on, and other stuff like that.
I'm not saying it can't or shouldn't be done, but I don't see the point in reinventing the wheel in this case by setting up a harder to use more intricate system. We run a stock tank heater all winter for our horses as well as heating the chin house, and we still use a lot less electricity in the winter.
A: If you run 1,500-watt stock tank heaters for two hours a day for five months, you're paying about $57 a year per heater. Unfortunately, alternatives are in short supply. Using a bubbler in this climate would not guarantee an ice-free tank and the cost of buying and installing solar-powered heating equipment outweighs the savings on your electric bills.
But there is good news. Your answer is not in your heater but in the tank. You can keep the tank water above freezing longer by using an insulated tank with an insulated cover that leaves only part of the surface exposed for watering. You also can partially bury the tank in the ground and insulate the ground around the tank. These approaches will lower your electricity costs by reducing the amount of time your heater runs. A stock tank heater set up this way will be more energy-efficient
That's appx $10 per month, of course depending on how long it's on, how cold the temps get, how large the tank is, etc.
