coverhvac
I'm living in co-op building in northeastern part of Queens, New York and have heat/AC unit in the apartment.
Two questions:
If you're not too concerned about aesthetics, you can use some flexible duct (or dryer duct) and a couple boots.
Use some foil HVAC tape to connect one boot to the duct on the ceiling, and then put the other boot on the ground, and use foil tape to connect the boots to the flex duct.
You can get boots that are straight, 45, 90 degrees, and horizontal or vertical, and many sizes -- the box stores all have lots to choose from.
You can also stick a grill on the bottom, just to make it look a very slight amount nicer.
Chlorine & Copper
You will have to keep your chlorine and acidity levels in constant harmony, otherwise the acidity will corrode and pit your copper tubing. Using aluminum would be exponentially worse. It the cooler your pool water gets, the worse effects it would also have on the copper. You can find good information from the EPA.
BTU's
A BTU is a British Thermal Unit. It takes one BTU to increase the temperature of one pound of water by one degree Farenheit. The average swimming pool is 20' x 30' x 5'. That would mean that the average swimming pool is about 22,500 gallons of water. Since one gallon of water weighs 8.34 lbs., the water in an average sized pool would weigh 187,650.
That means it would take 187,650 BTU's to increase that pool temperature by one degree. Since you would only have about 10% of that amount of BTU's required - it is very likely that the pool would simply absorb and disperse the heat transferred from your residence and never actually raise the temperature of the pool. Gullberg & Jansson has some great information on their website about heating pools.
Refrigerant and Line Set
In general it would take about 0.6 oz of refrigerant for each foot of copper tubing above 15'. Different manufacturers have different specifications of course. Considering it is a window unit, it would already have less refrigerant than say, a mini split unit.
The average 1.5 ton, or 18,000 BTU, mini split unit take about 3-4 lbs. of refrigerant and usually have about 15' of line set available 'in the box.' Depending on how long your copper tubing would be, you could be seeing so much heat loss just within the copper tubing itself, it would never "make it" to the pool. Plus, all of the possible extra refrigerant would be so hard on a compressor that small, compressor failure would always be right around the corner. Some good information can be found at ACHR News.
Legal Activity
In order to 'work' with Refrigerant, in fact, even buy (most) of it, you have to be EPA Section 608 Certified. There are 4 types of certification. There is Type I, Type II, Type III, and Universal. There is also EPA Section 609, but that is for motor vehicles. Without certification, you run the risk of EPA prosecution. And before you think that you will never get caught, there is a reward for turning people in. Information can be found at the EPA website.
Tools You Need
As you can see, there is a lot of specific tools and machines that you need to perform the job, not only legally, but safely. They are also very expensive to the average person. It is not uncommon for a vacuum pump to cost between $150 - $500. You can double and triple that cost for a Recovery Machine. There is a reason that most technicians work for a company that provides all of the tools required. It is hard to start off in the industry self-employed when you require certifications and tools that all cost money.
Conclusion
I would find a local HVAC/R Technician and run the idea across him. Ask him to come out and see what the job would entail. Ask him for advice. Ask him for a material cost and/or a list of what it would take to get the job done. Remember, this is only estimate stuff - because he may just tell you it isn't worth it, isn't possible with the equipment provided, or would be much more hassle than the intended benefit.
You could hire me to do it! But that would cost you a plane ticket, a case of beer, and a good home cooked meal before I even consider it.
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Best Answer
It's called a "fan-coil unit" and it seems to be missing a front panel as its majority cause of ugliness.
Start with your building superintendent or maintenance person/department.
[Fan Coil Unit: a unit with a coil through which heated or chilled water is passed depending on the season, and a fan to blow air across that coil to heat or cool the apartment.]