In a large pot, soak corn in water for 1 hour. Snip enough thyme leaves to equal 2 teaspoons. In a small bowl blend the butter and snipped thyme. Shape in a 4-inch log. Wrap in plastic wrap and refrigerate.
Remove corn from water. Remove silks by peeling back, but not detaching, the husks. Spread corn with some of the thyme-butter. Sprinkle with salt. Pull husks back around corn, adding several sprigs of thyme to each ear of corn.
Grill corn on the rack of a covered grill for 20 to 30 minutes or until kernels are tender, using tongs to turn and rearrange ears three times. Serves corn with slices of thyme butter.