Insert 4 wooden skewers (1 at a time) through each onion about 1/2 inch apart to create horizontal segments. Cut onions into slices between skewers. (Leave skewers in place to hold onion slices together during marinating and cooking.)
Place slices in a shallow container; add wine. Cover and chill 8 hours, turning occasionally. Drain.
Melt butter in small saucepan; stir in thyme and pepper. Brush onion slices with butter mixture, reserving some for basting.
Grill onions, covered with grill lid, over medium-high heat (350° to 400°) 6 to 10 minutes, turning and basting often with reserved butter mixture.