Heat a grill to medium-high heat. Grill the corn in their husks until the husks start to blacken, about 3 minutes per side.
Mix together the butter, chili powder, cayenne pepper, lime juice and some salt and black pepper in a bowl until incorporated.
Peel back the corn husks, leaving on to use as handles while eating. Rub the chili-lime butter all over the corn. Garnish with the cotija cheese.