I'd leave it open around the clock. For the time during the day the pool is cooler than the air, the sun will warm the pool with or without the cover. IMO the debatable difference between the 2 isn't worth the worrying about it. For the bulk of the 24 hour period, you'll be losing heat. Keeping it running will make more surface area for evaporation to occur with all the ^^^^^^^^^^ ripples.
As said above the deck jets will come in handy for once overnight.
They'll raise the Ph though so keep an eye on that.
As said above the deck jets will come in handy for once overnight.