Position an oven rack one level below the center of the oven, then preheat the oven to 350°F (175°C).
Combine the room-temperature butter, minced garlic, thyme, a small amount of salt, and ground black pepper in a small bowl. Stir until the seasonings are evenly incorporated into the softened butter.
Remove the neck and giblets from the turkey cavities. Inspect the skin and remove any remaining pin feathers.
Fold the wing tips beneath the turkey so they are less likely to become overly browned during roasting.
Season the interior cavity with salt and ground black pepper.
Using the handle end of a wooden spoon, carefully loosen the skin covering the breast without tearing it. Spread the garlic-thyme butter beneath the loosened skin, distributing it evenly over the breast meat.
Season the outside of the turkey generously with additional salt and ground black pepper.
Place 1 tablespoon of all-purpose flour inside a turkey-size oven roasting bag. Shake the bag thoroughly so the flour is dispersed over its interior.
Set the prepared oven bag inside a roasting pan.
Arrange the celery pieces, onion chunks, and carrot sections along the bottom of the bag, forming a vegetable bed.
Position the seasoned turkey directly on top of the vegetables inside the oven bag.
Secure the oven bag using the supplied oven-safe tie. Make six small openings across the upper surface of the bag to allow steam to vent during roasting.
Keep the loose ends of the bag tucked securely within the roasting pan.
Roast a 12–16 pound turkey for approximately 2–2 1/4 hours. For a 16–20 pound turkey, roast for about 2 1/4–2 1/2 hours. A 20–24 pound turkey will generally require 2 1/2–3 hours.
Check the internal temperature in several areas before removing the turkey from the oven. The thickest portion of the breast should register 165°F, while the thigh should reach 175°F.
After roasting, allow the turkey to rest for 20 minutes. This resting period permits the juices to redistribute through the meat before carving.
Carefully open the top of the roasting bag, taking care around the hot steam. Lift the turkey from the bag and transfer it to a carving board.
Carve the rested turkey into portions and serve.