Is it possible for thyroid cancer metastasize into only one part of the body?

Sort of: When a tumor metastasizes, it usually seeds multiple organs in the body. Not all of the seeded sites may develop obvious metastases, so it may appear that only one site, the one with a large tumor, is involved, but many other sites are likely to have sub-clinical metastases.

Yes: Often well-differentiated thyroid cancer will only go to neck lymph nodes, this is then removed and radioactive iodine treatment is given. Most of the time the patient's prognosis continues to be excellent. If it has metastasized to multiple areas or cannot be resected, then radioactive iodine may be the only option. Prognosis is still good with well-different. Thyroid cancer in that situation.