I live in South Florida and have a pool that isn't screened. I also have several Live Oak and Pine trees. I spend a lot of time skimming and cleaning the pool. Most of my problem is with floating leaves. On a windy day more leaves can fall while I'm at work than the skimmer can handle. A lot more. So I end up with the skimmer clogged and a billion leaves to skim.
I don't have a lot of problem with the pool getting too warm. Today it's at 82, which is as hot as I've measured it in 10 years. Typically it stays below 80. For about 6 or 8 months of the year, I wouldn't mind raising the temp a few degrees.
I'm toying with the idea of putting on a floating solar cover - more to catch debris than anything else. But I'm not sure how effective that will be. I'd be leaving it on 24/7 except in the depths of summer (like now).
But I'm trying to figure out how having a billion leaves on a floating cover is going to be any easier to deal with than a billion leaves in the pool....