Preheat grill to medium-high.
Rub ears of corn with cold butter (easier to coat the raw ears of corn evenly)
Grill corn for 15 to 20 minutes, until tender, turning a couple of times to char evenly.
Meanwhile, in a small bowl whisk chili powder into mayonnaise and set aside.
Transfer corn to a serving platter and slather each cob evenly with chili mayonnaise. Sprinkle cotija, cilantro, and smoked paprika over cobs. Serve with lime wedges.