Preheat oven to 375°.
In a large bowl, stir together carrots, ¼ cup oil, 2 tablespoons thyme, 2 tablespoons turbinado sugar, 2 teaspoons salt, and 1 teaspoon pepper. Place on one side of a large rimmed baking sheet.
In the same bowl, stir together beets, vinegar, remaining ¼ cup oil, remaining 2 tablespoons thyme, remaining 2 tablespoons turbinado sugar, remaining 2 teaspoons salt, and remaining 1 teaspoon pepper. Place on other side of baking sheet.
Bake until vegetables are tender, 40 to 45 minutes. Garnish with thyme, if desired.