No, there is no diet that is recommended to help with hypothyroidism. Some foods can interfere with absorption of synthetic thyroid medication, so you do need to watch out for those. The Mayo Clinic has more on this here. It seems unlikely to me that this coldness in your extremities is related to the thyroid disorder. Are they cold when other people touch them, or do they feel normal to other people? This may not be neurological. Can you get in to see your GP for a referral soon?