Heat olive oil in a skillet on medium heat. Add mushrooms and sauté for 1 minute. Add red wine, salt, pepper and thyme. Sauté, stirring often, until liquid has been absorbed by mushrooms (about 10 minutes). Remove from heat.
In a large salad bowl, add arugula and tomatoes. Cover arugula with warm mushrooms. Toss salad with red onion, blue cheese, croutons and balsamic vinegar. Serve immediately.