Hyperthyroidism happens when there’s too much thyroid hormone in your body. This condition is also called thyrotoxicosis. An overactive or enlarged thyroid gland may produce more thyroid hormone.Enjoy home-cooked whole foods on a low-iodine diet. Avoid restaurant, boxed or processed meals, and prepared sauces and marinades. These may contain added iodine. If you’re on a low-iodine diet, it can be more difficult to get enough vitamin D and calcium. Talk with your doctor or dietitian about taking supplements for these nutrients.