First of all this is NOT intended to be medical advice.
I have been on Synthroid since around 2003. Back then I had changed doctors 3 times and they all said to see a shrink. My shrink admitted that my fingers were blue but he said I was causing it out of my felt need to be sick. They sent me to a heart specialist who said there was nothing wrong with my heart but my fingers were blue. Then a blood test revealed that my TSH was real high so they put me on synthroid. My temperature jumped from 96 to 98 degrees and 15 years of constipation was finally resolved.
I wish that was the end of the story. However it gets a lot more complicated at this point. Synthroid is T4 and you need T3 and T4 to operate. The theory is that excess T4 is converted to T3. Your brain needs T3 to operate. The amount of T3 and T4 you need varies with the temperature outside and the amount of stress you are under. So after tracking my thyroid status by the constipation I discovered that it actually shows up quicker as depression/paranoia. In fact my brain totally shut down before my fingers turned blue again. Then I took an extra 1/2 dose of synthroid and the depression lifted like magic.
I have long felt that people on synthroid need a better method of tracking their medicine. People with diabetes check their blood sugar three times a day. So I got the idea of tracking my temperature. Over a few days of taking my temperature three times a day, I concluded that it is 96 in the morning, 94 in the afternoon, and 98 in the evening. I have like a "hot flash" almost every evening, and I am a guy! I checked and if it goes below 93 degrees you need medical help. The low reading of 94 corresponds with every muscle aching, being stiff as a board, and being depressed. In fact I sometimes had "panic attacks" that also seem to be from the low temperature. It is like getting on an airplane and remembering that you forgot to pack your suitcase.
What is the solution? I do not know. I think the doctors should keep the TSH real low so that you have excess T4 to convert into T3. Another possibility is to take a Thyroid supplement like Kelp that is a source of natural Iodine, as well as thyrosine, Irish Moss, and some other stuff in it.
Having a low body temperature also leads to chronic illness. This winter I had a cold for 6 weeks before going to Asia. There it quickly resolved. After being back a few weeks it started coming back. The reason you get a fever when you are sick is because raising your temperature kills bacteria. Lowering your temperature allows the bacteria to thrive.