Preheat oven to 500°. Toss together first 3 ingredients, 1 Tbsp. olive oil, 1 Tbsp. vinegar, 1 tsp. salt, and 1/2 tsp. black pepper in a medium bowl.
Toss together beets, next 2 ingredients, 1 Tbsp. olive oil, 1 tsp. salt, 1/2 tsp. black pepper, and remaining 1 Tbsp. vinegar in a large bowl. Place beets in a single layer in center of a large piece of heavy-duty aluminum foil. Bring up sides of foil over beets; double fold top and side edges to seal, making a packet. Place packet in 1 end of a jelly-roll pan.
Bake beets at 500° for 15 minutes.
Meanwhile, cut 1 orange half into 6 wedges. Squeeze juice from remaining orange half to equal 1 1/2 Tbsp. Cut tops from carrots, leaving 1 inch of greenery on each. Toss together carrots, orange juice, orange wedges, thyme sprigs, and remaining olive oil, salt, and pepper.
Remove pan from oven, and place onion mixture and carrot mixture in pan next to foil packet, spreading in a single layer. Return to oven, and bake beets, onions, and carrots 25 minutes. Cool 10 minutes; combine vegetables, and serve immediately.