While hypothyroidism is fairly common in dogs, and is more prevalent in some breeds, it is a comparatively rare disease in cats, hardly ever occurring "naturally." In fact, the most common causes are the result of either surgery or radioactive iodine treatment for hyperthyroid cats. It should be mentioned that in both cases, the odds of the treatment resulting in hypothyroidism are very low. The latter was the case with my Bubba, who received radioactive iodine therapy for hyperthyroidism, and subsequently turned hypothyroid.
Fortunately, hypothyroidism is not life-threatening, although it can lead to a lower quality of life. It is easily reversible, though. Read more about the causes, symptoms, diagnosis, and treatment of hypothyroidism in cats.

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Franny,
How did Bubba do after his radioiodine treatment? I see that he did become hypothyroid. Did it affect his kidneys? Was the hypothyroidism easy to reverse? My 15 year old kitty is in a similar situation as Bubba was – on Tapazole for over a year and no longer responding to it (and it’s been causing anemia). He does not have CRF, but his specific gravity is on the lower side and we think it is in his future. Strongly considering radioiodine to get him off of Tapazole (vet still feels he is a good candidate for a low dose of radioiodine) and hopefully resolve the hyperthyroidism and anemia. My biggest concern is him becoming hypothyroid and moving into active CRF. Not sure if thyroid supplementation can reverse that. Would love to know what you did with Bubba.
Many thanks for your insight.
Bubba was never diagnosed with CRF. However, I suspect there may have been some undetected heart involvement. He recovered quite well from the hypothyroidism with thyroxine; gained weight, with bright eyes and a shiny, healthy coat. However, about nine months later, after a series of E/R visits, and followups with his own vet, he was completely incapacitated by thrown blood clots to his legs. He was PTS on December 5, 2005.
I’d suggest talking with your vet more. If he is convinced your cat is a good candidate for radioiodine, statistically, there is only a 1% to 5% chance of going hypo. Even then, hypothyroidism is not considered a fatal disease and is emminently treatable. OTOH, untreated hyperthyroidism can be fatal. Ask your vet if he agrees with my theories.
Thanks for your reply, Franny.
I am sorry to hear about the blood clots Bubba experienced and that he had to be PTS. Did they ever figure out what caused them?
He was a very lucky cat to have you as his parent.