OK; let's talk about some general numbers.
Assuming an in ground pool - the water temperature will stabilize at somewhere between ground temperature in that area and any solar heat gain - Less all the night time heat losses.
Whew! Let's just call it 70Âş water in the unheated pool. <g>
6000 gallons of water weighs about 50,000 lbs. The specific heat of water is 1.0 So each degree of temperature increase will require adding 50,000 BTU's of heat to the water. So if you want the water to be 80Âş (ten degrees warmer) you will have to add 500,000 BTU's. If you are adding 50,000 BTU's per hour - it will take ten hours of continuous heat pump operation to accomplish.
But . . . . you also have to add all the BTU's which are being lost during the time you are heating the water. The BTU's you add don't just accumulate - they immediately start to escape. This is why you cannot add BTU's too slowly - the BTU's will escape faster than you can add them. And this is why fueled pool heaters are 300-700K BTU's - so the pool can be heated quickly enough to overcome all the heat losses.
Using the building's AC to heat the pool water is even worse - because any time you need to be heating the pool - the AC is not going to be running 100% of the time. <g>
PHM
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If I recall correctly from when the pool was set up last summer it is just over 6,000 gallons