On my last batch, I did my partial mash the evening before. Collected the wort in a sanitized bucket fermenter, and put a lid on it. Boiled it the next day and didn't have any problems.
It would take quite a while for wild yeast or bacteria to build up harmful numbers/ruin the wort, and boiling it kills any of the few cells that might have gotten in there. You could boil it briefly and then tuck it in for the night, but don't think it would be necessary.