Arrange oven rack to upper portion of oven and heat to 425°. In a large roasting pan, arrange citrus to form a bed for the fish, reserving a few slices. Wash fish and pat dry. Score each side of fish in 1-inch intervals, about ½ inch deep. Season inside of cavity with salt and pepper and fill with thyme and reserved slices of citrus. Rub fish with 2 tablespoons oil and stuff each score with a slice of butter.
Transfer fish to prepared pan, drizzle with remaining oil and roast until firm and flesh is moist and opaque, 30–40 minutes. To serve, gently lift off the top fillet, leaving as many bones behind as possible, then remove the spine from the bottom half and scoop away fresh. Spoon pan drippings over served fish.
Red Snapper provided by Big Water Fish Market; 6641 Midnight Pass Rd, Siesta Key; 941.554.8101