Basically you're capturing the sun coming through the window at the sheet, heating it up so that it feels noticably warmer and radiated some of that heat to the air inside. The alternative is to just let the sun come through the window and spread out hitting the floor and other things in the room. Same amount of energy in, just more spread out so the warming effect won't be as obvious to feel and measure.
It's possible that the sheet is stopping some of the energy from being reflected back out of the window but the percentage lost with out the sheet is so low I'd be surprised if it makes a measurable difference. At night the sheet will definitely help by providing insulation over the windows. I always close the curtains at night during the winter. and we've been slowly replacing all of them with good thick curtains to improve R-values of the windowed areas.
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