Stir the mayonnaise, cranberry sauce and mustard in a small bowl.
Thoroughly mix the turkey, picante sauce, cilantro and thyme in a medium bowl. Shape the turkey mixture into 8 (1/2-inch thick) burgers. Place 1/4 cup cheese in the center of each of 4 burgers. Top each with another burger. Pinch the edges of the burgers to enclose the cheese.
Lightly oil the grill rack and heat the grill to medium. Grill the burgers for 10 minutes or until desired doneness, turning them over once halfway through grilling. Grill the orange slices for 1 minute, turning them over once halfway through grilling.
Spread the mayonnaise mixture on the top halves of the buns. Place the burgers on the buns. Top with the orange slices, onion and lettuce.