Preheat the oven to 350°. Grease a 9-by-13-inch baking dish. Pour 1/3 cup heavy cream into the dish. Place a layer of overlapping potato slices on top and season with salt, pepper and thyme. Add a layer of apple slices, sprinkle with one third of the cheese, some thyme, salt and pepper. Repeat the layering two more times, pressing the layers down with your fingers so the cream works its way into each layer.
Cover the dish loosely with foil and bake until the potatoes are tender when pierced with a fork, about 1 1/2 hours. Uncover the dish and cook under the broiler until the top is golden, about 3 minutes.