Combine oil, chili powder, cumin, thyme, salt and pepper in saucepan. Bring to boiling. Reduce heat; simmer 5 minutes. Add vinegar. Cool slightly.
Place meat in large, plastic food-storage bag. Add 1/2 cup of the marinade; seal. Refrigerate overnight, turning occasionally. Refrigerate remaining 3/4 cup marinade for dressing.
Drain steak, reserving marinade. Grill or broil steak 4 inches from heat, or cook in grill skillet over medium-high heat 6 minutes or until desired doneness; turn and baste once halfway through cooking. Discard remaining marinade used as brush-on.
Let steak stand 5 minutes. Cut across grain in very thin slices. Toss with corn, beans, tomatoes and the 3/4 cups reserved marinade in large bowl. Arrange lettuce and radicchio leaves on platter. Top with salad. Makes 4 servings.
