Add onion, celery and carrots to the sausage and cook till tender. Add thyme and stir.
Add broth and rice and bring to a boil. Reduce heat to bring soup to a slow simmer. Cook till rice is tender (depending on the wild rice blend you use times may differ, but 30 minutes is around the time it takes to cook).
Whisk cream and flour together and add to soup. Stir.