Start the coals or heat a gas grill for medium-high direct cooking. Make sure the grates are clean.
Pat the fish dry with paper towels. Brush them with oil and season with salt and pepper on both sides and in the cavity. Tuck in the thyme sprigs—or wait and scatter them over the fish after turning.
Put the fish on the grill directly over the fire, at an angle or perpendicular to the grate. Cook, turning once, until the skin is charred in places and the fish release easily, 2 to 4 minutes per side, depending on their size and how hot the fire is. The easiest way to test for doneness is to insert a skewer or thin knife through the thickest point. If it goes in without resistance, the fish is done. Transfer the fish to a platter and serve with lemon wedges and a final sprinkle of salt.