Trim the fat from tenderloin. Combine 3 teaspoons thyme, salt, and pepper; rub evenly over tenderloin. Cover and chill 2 hours.
Combine 2 teaspoons thyme, mushrooms, wine, broth, and garlic in a large saucepan, and bring to a boil. Reduce heat, and simmer until reduced to 1 1/2 cups (about 1 hour). Combine water and cornstarch, and stir into wine mixture. Bring to a boil, and cook 1 minute, stirring constantly. Remove wine mixture from heat; set aside, and keep warm.
Preheat oven to 400°.
Heat oil in a large nonstick skillet over medium-high heat. Add tenderloin, browning on all sides, about 12 minutes. Place tenderloin on a broiler pan coated with cooking spray. Insert meat thermometer into thickest portion of tenderloin. Bake at 400° for 20 minutes or until thermometer registers 145° (medium-rare) to 160° (medium). Place tenderloin on a serving platter, and cover with foil. Let stand for 10 minutes. Serve with Beaujolais jus.