I second the suggestion of hard and harmless fences (as opposed to venturing into the desert and dying). If players must explore the whole map, they expect it to be not only finite, but not diluted by large amount of useless empty space at the borders.
You just need appropriate warning messages; apart from the previous good suggestions, consider breaking the fourth wall with words (e.g. "Thank God, you have nothing to do in the Desert of Skulls. Maybe in a sequel.") or graphics (e.g. a thick red line on the ground, matching the position of an invisible wall).