Preheat oven to 325°.
Unroll roast; trim fat. Reroll roast; secure at 1-inch intervals with heavy string. Combine preserves, mustard, and thyme in a bowl; stir. Brush 1 tablespoon apricot mixture over roast. Place on a broiler pan coated with cooking spray. Insert meat thermometer into thickest portion of roast.
Bake at 325° for 1 hour and 45 minutes or until meat thermometer registers 160° (slightly pink), basting once with apricot mixture. Let stand 15 minutes before slicing.
Bring remaining apricot mixture to a boil; reduce heat, and cook 2 minutes. Serve with roast.