For the most part, drying will set the fabric, so what you see is what you'll get. However, if you are able to air-dry your clothes outside, the ultraviolet rays of the sun act as a natural whitener. (This method works best if you used lemon juice in the washing process — just as putting lemon juice in your hair in the Summer can make you blonder, the same works for clothes!)
White-Hot Tip: Clotheslining your garments in the direct sunlight for a few hours should be enough, but to make them even whiter, feel free to put them back out for a few hours another day. Just don't leave them out for days at a time, as that can weaken the fabric.