I was never 'cold' on a regular basis, - just cold sensitive, as in I could not stand frigid weather or too much AC.
The symptoms are not by the book, meaning they don't show up in everyone, there may be some for some people and some for others and a combo for yet other groups. You are doing right IMO - by listening to your body.
Your body is ALWAYS your best friend in this journey.
You may try other options, as you said - some
Iodine may be it for you, or the "Moreless" way of taking a lot of seaweed, but whatever it is, it is your body that will guide you.
Personally, I took the seaweed route - [hypo was my first forage into CZ] (Modifilan) and I'd try that again if I needed to. It was gentle, and excellent in other ways: chelating mercury and not being something that you need to take for life. Have tried many other things in my ride through these last couple of years and I'm happy to say that simple always wins in the end.
The thing is, like sailing - it is all a balancing act. You can take something to get you back on the right path, and then you have to provide the body with the right fuel and support - mental, and otherways, to let the body do what it has done all our lives: carry us along this journey with strenght and dignity. We should tell our bodies how much we love each and every part of it each and every day.
You know, the researchers do wide all inclusive reporting, your body is your very best barometer.
Good sailing to feeling well...
MadArt (ist)
PS After Modifilan - ML provided a lot of good information on mineral balancing and food choices, as well as an easy maintenance system to support the body while making adjustments and trying things that resonated with me.
Though a controversial site - there is a lot to learn in his forum, if you are not afraid of a plate thown at your head once in a while for not paying attention:)
Also, old posts have a wealth of invaluable information and kindly shared expertise and advise. (Owen, Lapis, ...)