Your cat will likely go through a lot of testing to properly diagnose their disease and determine your cat’s overall health. For the remainder of your pet’s life you will be giving daily medication oral or transdermal methimazole to treat your cat’s condition.
Your veterinarian may discuss switching your cat to a low iodine diet like Y/D made by Hills Veterinary Diets.
There are also radioactive iodine treatments that can be performed by a specialist if you and your veterinarian feel that your cat is a good candidate for this kind of treatment. This treatment may eliminate the need for daily medications. Surgery to remove the thyroid nodule was a treatment option in the past, but is rarely performed today.