I'm trying to think back to when I lived in Oklahoma. I certainly remember some summer nights being very very warm, to the extent you wouldn't even want a sheet. However I also remember that cold fronts could move in quickly and drop the temperature 20 degrees in a few hours. I'd be slightly leery of bringing just a sheet, but it depends how warm you sleep as well. I think if it were 65, I'd already be slightly uncomfortable with just a thin sheet, much less below 60.

You could get a fleece sleeping bag liner that might be warmer that weighs around half a pound (using weights quoted by REI) and probably would get you below 60. Of course they also seem to be unreasonably expensive. If you have a fleece blanket lying around you might be able to MYOG a quick quilt by cutting out a piece and sewing up a quick footbox... I can't imagine it would weight more than a pound...