Not sure if it’s helpful at this point, but Steve Phinney wrote this blog post on just this subject.
Does your thyroid need dietary carbohydrate?
Here’s an section of it:
To the casual observer, this reduction in active thyroid hormone (called T3) has been taken as evidence that carbohydrate restriction impairs thyroid function. Some have opined that carb restriction should never be maintained below 100 grams per day in order to prevent this effect. Others advocate that people on a low-carbohydrate, high fat (LCHF) diet take intermittent “holidays” from carb restriction to boost thyroid function back up to “normal.”
An alternative explanation for these changes in thyroid hormones when one is weight stable on a LCHF diet is that the body becomes more responsive to these hormones due to beneficial changes in cell structure and function when in nutritional ketosis. As a result, it can function normally at lower T3 levels. Put another way, a ketogenic diet seems to result in improved thyroid hormone sensitivity (i.e., it takes less hormone to produce the same effect), which, if anything, puts less of a burden on thyroid hormone (T4) production in the thyroid gland and its conversion to T3 in the liver.
Is this hypothesis (Yes, Virginia, it is only a hypothesis) of improved thyroid hormone sensitivity on a ketogenic diet far-fetched? In fact, it has been repeatedly demonstrated that a well formulated ketogenic diet improves insulin sensitivity, often dramatically so in people with insulin resistance or type 2 diabetes. There is also strong evidence that the brain’s sensitivity to the satiety hormone leptin is improved during nutritional ketosis as well. Thus an improved thyroid hormone response during a LCHF diet would be quite consistent with these other documented improvements in hormone sensitivity.
How many published studies from well designed, prospective human trials have shown that impaired thyroid function (i.e., hypothyroidism) occurs on a ketogenic diet? The answer to this question is quick and simple – NONE!