Preheat oven to 325 degrees. Slice tomatoes in half lengthwise and gently squeeze out seeds or scoop them with a spoon --leave as much as the flesh as possible.
Flip scooped tomatoes over and make a small incision in the back of each to allow a place for cooking juices to exit, and promote caramalizing.
Add olive oil, balsamic vinegar, thyme and salt to bowl, whisk together. Gently add tomatoes and toss to coat.
Lay the tomatoes, cut side up, in a single layer on a rimmed baking sheet. Reserve excess oil/balsamic mixture for later.
Roast tomatoes on center rack for 40 minutes. Increase the oven temperature to 425 degrees and continue to roast tomatoes about 20 minutes more, or until caramelized. Grape tomatoes may need to come out earlier.
Remove tomatoes from oven, drizzle with a bit of the remaining oil/balsamic mixture.