Cut the heart into 1/2 inch strips. Season with salt and pepper, and coat with flour.
Melt the butter in pan over medium-high heat. Add the beef heart strips and quickly cook until they begin to brown, about 1 minute. Stir in the onions, carrots, potatoes and thyme and continue cooking for 2 minutes. Add the beef broth and the red wine. Bring to a boil and then lower heat to reach a gentle simmer.
Place a lid over the pan and cook for 1 hour. Season the braise to taste with Salt and Pepper.