I thought that my thyroid would be a problem; since my hands and feet are always cold. My core is really warm; especially during sleep when my metabolism is well relaxed. But my body temp is generally low; and my basal temp average is low. Nothing else about me is normal for the general public; so I'm not sure about these averages.
I did try thyroid glandular many years ago. Like you, I don't trust what the glandulars do after long term use. I just wanted to see if it helped my thyroid. It did not help. Then I tried iodine megadose for 5 months. No help there either.
I think I will stick with nettle, seaweed, ashwagandha, and any other herbs that help the endocrine system.
But I'm more convinced that it is started by the adrenals.
You definitley have hypothyroid symptoms, which can also cause the constipation. And poor adrenal function is one cause of hypothyroidism. Hormones are also another common cause. Either way working on the adrenals will help. Bitters and B vitamins will also help if it is hormonally related.