If one ignores the factors of heating from sunlight, cooling from evaporation, and ground temperatures, then the pool water should average around the average temperature over the 24 hour period assuming there aren't huge temporary spikes or drops in such temperatures. That gives you a baseline -- it doesn't tell you how long it takes to get to this average if you are starting with water at a different temperature.
If you cover the pool at night (or use a clear cover all day and night), then you create an asymmetry where more heat is gained during the day than is lost at night and this can easily add 10F or more to the pool temperature.
My own pool over the winter pretty much averaged out to the average temperature throughout the day and night -- perhaps a little higher than that -- and I had an opaque cover on it almost all of the time. The lowest it dropped was to 45F when the daytime temp was in the low 50's and the nighttime temps was in the high 30's. During the spring/summer/fall (part of those times, at least) we use solar heating and keep the pool at 85-88F with daytime temps of 70-90F and nighttime temps at 50-65F.
Richard
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