By low thyroid, I presume you mean underactive or hypothyroidism which is confirmed by a high TSH (thyroid stimulating hormone). This is usually suspected in patients w/abnormally low energy, unexplained weight gain, change in skin texture & hair, constipation, cold intolerance, high cholesterol, etc.
Hypothyroidism is treated by taking levothyroxine or T4. TSH should be monitored 6 weeks after starting or dose changes. It should be checked twice to be sure you're not making a trend in one direction or another.
You don't want too much levothyroxine since that can lead to hyperthyroidism or an overactive thyroid associated w/jitteriness, tremors, palpitations, sweats, weight loss, and atrial fibrillation in extreme. In the long term, an overactive thyroid can also lead to bone loss or osteoporosis, while the atrial fibrillation can increase one's risk for stroke.
Therefore, just like Goldilocks, you want just the right dose of levothyroxine for you, whether your TSH is towards one end of the normal range or the other. By the way, some physicians might suggest taking liothyronine or T3 which is the active form of thyroid hormone (T4 is the inactive form). Typically levothyroxine & liothyronine is synthesized and is considered bio-identical to what your thyroid (used to) make, even though it's not "natural".
Some physicians recommend "natural" dessicated (dried) thyroid hormones derived from pigs since this contains both T4 and T3. However, many would argue that while dessicated thyroid is natural to a pig, it may not be natural to you & me. Furthermore, depending upon your perspective, the ratio of T4:T3 varies from pig to pig.
Don't forget that while we used to use insulin derived from pigs, we've since moved over to bio-identical insulin synthesize by E coil & yeast. We still use porcine heart valves but there's much ongoing research for a better substitute.
Hope this helps!