There are pool heat calculators on the net that can give you the answers for gas heat alone. You would need to get in touch with a pool contractor to see the costs and tradeoffs for the various heating methods.
Solar, heat pump, gas and electric are all used in TV.
My pool with no cover and solar only was 86 yesterday.
When I had a cover on the pool it was over 80 on some days in January.
I found the cover too hard to remove and not worth the effort.
If I were building a pool from scratch I would only have a rectangular pool with an automated cover.
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