Cook the white rice according to package instructions. Set aside.
In a large pot, sauté the finely chopped onion, diced carrots, and chopped celery until they become tender.
Add the shredded cooked turkey and dried thyme to the pot. Season with salt and pepper to taste. Stir well.
Pour in the chicken broth and water. Stir to combine. Bring the mixture to a gentle boil.
Reduce the heat to low and let the soup simmer for about 20-25 minutes, allowing the flavors to meld together.
Pour in the heavy cream and cooked white rice. Stir until the soup becomes creamy and well-blended.
Taste the soup and adjust the seasoning with more salt and pepper if needed.