You can use any type of radish or beet; varied colors make for a more stunning presentation.
Preheat oven to 450 degrees. Line a piece of foil with parchment. Place beets in the center, fold in half, and fold edges. Place on a baking sheet and roast until tender, about 1 hour. Unwrap beets, let cool slightly, then peel. Cut beets into quarters.
Place vegetables in a medium bowl. Drizzle oil and lemon juice on top. Add thyme, season with salt and pepper, and toss gently. Divide salad among 12 three-ounce paper nut cups, and serve immediately.