Is hyperthyroidism is curable?

Depends on cause: 3 common causes of spontaneous hyperthyroidism. Overactive nodular goiters produce more thyroid hormone over time, and need to be medically or surgically treated. Graves' is autoimmune disease that can go into remission (temporary cure) but usually after taking anti-thyroid rx for while. Inflammatory thyroiditis is self-resolving condition that may lead to hypothyroid. Answer depends on which type.

Indeed: The treatment of hyperthyroidism depends on the cause. Sometimes its self limited. Sometimes it can be cured by surgery and sometimes radioactive iodine treatment. It is however almost always curable.