Preheat oven to 450°. Cut carrots crosswise in half and then lengthwise into 1/2-in.-thick sticks. Toss carrots with oil, salt, pepper, and thyme; spread evenly in a greased 15x10x10-in. baking pan.
Roast until tender and lightly browned, stirring once, 12-15 minutes. Toss with cheese.