Extended low carbohydrate diets are known to lower levels of T3.  (I think
that is the one from memory).  T3 is the far more active from of thyroid
hormone (compared to T4).  This effect is discussed somewhat using the
medical literature in Rob Fagin's 'Natural Hormone Enhancement' book.  A
solution is to mix a largely low carbohydrate diet with periodic high
carbohydrate feedings to keep T3 in 'normal' ranges.  Fagin recommends a
carbo feedings every three/four days of low carb diet.  Personally, I eat a
relatively high carbo diet every Friday night/Saturday with the rest of the
week low carb.  It works for me; weight loss and weight control.

Kind regards,

  Wade

P.S.  I am replying a bit late after out for the night with an old friend
visiting from out of town.  I wanted to respond while this was fresh in my
mind lest I let it slide.  If you have any questions please post them as I
would be happy to respond in a more coherent fashion when I'm well rested.
;)  I have not been diagnosed with thyroid problems by I do seem to respond
better to periodic high carb feedings on a generally low carb diet with
respect to weight control and general feeling of well being.  YMMV.