Preheat a wood-burning or regular oven to 500 degrees. (If using a regular oven, set rack in lowest position and line with a pizza stone or metal baking sheet.) Combine oil, tomatoes, and thyme in a large ovenproof skillet. Roast (on pizza stone, if using) until tomatoes brown in places and release their juices, 25 to 30 minutes. Season with salt. Add cheese to skillet; return to oven and roast just until warmed through and very soft, about 5 minutes more. Serve immediately.