I have been having this for 2 years, was only diagnosed about 3 months ago.
Most pharmacists recommend taking thyroid replacement (synthroid or similar) meds in the morning. Some people on the forum have tried taking it at night and have had no problems. Others found that it increased the sleeplessness and caused other problems like heart palpitations and night sweats.
I don't think it necessarily matters when you take it as long as you take it the same time and the same way every day - with water, no food or vitamins to absorb the drug so your body doesn't get the benefit, etc.
Another thought - have you had your thyroid levels tested recently? From your comments, sounds like you could possibly be hyperthyroid from too high a dosage of the meds. That could cause insomnia and nighttime palitations. You might want to give your doctor a call if you haven't been tested recently.