One of the most effective treatments for metastases from thyroid cancer is a form of radioactive iodine known as 131-I. For more than 50 years, 131-I has been used to find and destroy thyroid cancer cells that have spread to other parts of the body. In many cases this treatment destroys the metastatic cells. However, in some patients it does not appear to work completely. This study is designed to use a slightly different form of radioactive iodine (called 124-I) which can precisely predict the amount of radiation that each metastatic lesion will receive.