As I describe in the thread Water Absorption and Heating from Sunlight, about 60% of sunlight gets absorbed to heat a white plaster pool. For a painted black pool, it would be well over 90% so would have a somewhat higher average temperature. However, an uncovered pool can lose a lot of heat through evaporation (and convection), especially if the air is dry and if there is wind. Use of a clear or light blue (not opaque) bubble-type pool cover can usually increase the pool temperature by around 10-15ºF. Solar heating can increase the temperature more, depending on the area of the solar panels. With a pool cover and solar combined, one can get the pool water to be 20-25ºF warmer than the average day/night air temperature (sometimes higher) during the summer. My pool near San Francisco has a mostly opaque thinner electric safety cover (so not as insulating as a bubble-type cover and not clear) but has solar panels with 94% of the pool surface area (though 2 panels are often in shade so solar is more like 74% of pool surface area). The pool target temperature is around 88ºF since it is used by my wife almost every day for therapy exercise.
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