Actually melatonin, produced by the pineal gland in your brain, controls your sleep patterns to a greater extent than the Thyroid does with it's secretions of T3 and T4. Your body has natural patterns called circadian rhythms, or "body clocks", that control the secretion of hormones in a relative pattern like clockwork. Melatonin is an example of a compound secreted in a clockwise fashion, more being secreted at night/dark and hence you getting tired, less is secreted in the morning/day hence you waking up and so on. This follows a rough 24-hour pattern, properly secreting higher or lower during those specific times of night and day. If that circadian rhythm for sleep is disrupted by say melatonin level fluctuations you can experience a change in sleep patterns like becoming more tired in the day even though you should not be.
However the thyroid should not be ruled out. Hypothyroidism, an underactive thyroid, is very common and one symptom of less T3 and T4 secretion is tiredness. Boosting the levels of thyroid hormone can make you less tired which is why the doctor will ask for a TSH level in blood work should you talk to a doctor about it. TSH, thyroid stimulating hormone, is the hormone secreted by the anterior pituitary gland that controls the output of the thyroid, low TSH means less thyroid output and hence the possible symptom of frequent tiredness. I have hypothyroidism and I am on medication for it, I am less tired than before however my condition is more directed towards being cold all the time.