If your broth is frozen, as mine was, microwave until warmed. Throw in the tomatoes and warm them too.
Heat the oil in a Dutch oven or soup pot and cook the onion about 5 minutes, stirring. Add the thyme and cayenne and stir, cooking another minute or two. Add the sliced sausage (I used a smoked beef but almost anything would be good), yellow pepper, celery, okra, rice, broth and tomatoes and bring to a simmer. Reduce heat, cover partially, and simmer about 20 minutes, stirring now and then.
Turn off the heat and stir in the shrimp. Cover and let stand 5 minutes until the shrimp is cooked through. I allowed about 7 minutes since my shrimp was frozen but if I'd thought ahead I would have run it under cold water to defrost first.
Stir and serve with the hot sauce at the table so everyone can make it as hot (or not) as they like.