Preheat oven 425 for 20 minutes. Clean entire fish, leaving head and tail intact. Place about 1 pound of salt on an oven tray or a heat-proof ceramic plate and place fish on top. Sprinkle fish with salt and place the thyme in the cavity. Cover the fish with the remaining salt. Bake for 15 minutes.
With 2 spoons scrape salt from the fish. Fillet the fish, discarding the bones. Divide fish and place on 2 plates. Sprinkle with olive oil and serve with seasonal salad and vegetables.