Pull down corn husks and remove silk. Place husks back over corn and soak in large bowls filled with cold water for 30 minutes.
Preheat a gas grill to medium. Drain corn on paper towels and pat dry, pull down husks and brush kernels evenly with butter. Place husks back over corn and tie ends with kitchen twine to keep in place. Arrange corn flat on grill with string ends away from direct heat and cook, turning often, until tender, 20 to 25 minutes.
Cut away twine and pull down husks. Spread mayonnaise on each ear, then sprinkle with chili powder and Parmesan. Serve with lime wedges and salt and pepper for seasoning.