Melt the butter in a saucepan. Add the lime juice, salt, and cayenne. Stir. Keep warm.
Now the corn: Peel off all but one or two layers of the corn husk. Pull the remaining husks down, but not off, and remove as much silk as possible. (Don't fuss with it too much; any remaining silk is easily removed later during Step 5). Pull up the husks; it's okay if some kernels aren't completely covered.
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 5 to 10 minute Then, you can push the corn to a cooler spot on the grill if you're cooking other things, or remove from the heat completely and set aside.
Just before serving, peel off the husk and brush away the 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 little chewy.).
Brush the warm cayenne butter on the hot grilled corn and serve.