Melt the butter in a small saucepan and stir in the lime juice, salt, and cayenne. Keep warm.
Peel off all but one or two layers of the corn husks. Pull the remaining husks down, but not off, and remove the bulk of the silks (the rest will come off easily after they char). Pull up the husks; it's okay if some kernels peek through.
Prepare a hot charcoal fire or heat a gas grill to high. Put the corn on the grate while the coals are still red-hot. (Cover a gas grill.)
Grill the corn, turning often, until the outer layer of husk is completely charred. Depending on your fire, this could take from around 5 to 10 minutes. You can push the corn to a cooler spot if you're grilling other things for your meal, or transfer the grilled corn to a platter and keep it warm in the charred husks.
Just before serving, peel off the husk and brush away any remaining silks. Brown the kernels on the grill briefly, turning the corn frequently to develop a roasty color and a little additional smoke flavor, about 1 minute. (If the corn spends too long on the grill without the protection of the husk, the kernels will become dry and a bit chewy.)
Brush the warm cayenne butter on the hot grilled corn and serve immediately.
Photo: Martha Holmberg