Here is my take on thyroid, this is based on personal experience and a lot of bloodwork. Thyroid levels change in response to many things, they can go up or down in response to diet, training, recuperation and supplements.
The average person's thyroid isn't producing much because they do things that suppress it. They don't eat balanced meals, they go too long between meals, they are stressed out, they take CNS stimulants (OTC, perscription, or just too much coffee). Exercise has been shown to effect thyroid also.
These people probably could "fix" their thyroid if they fixed what was suppressing it, it would take time though for TSH and T3 levels to go up.
Once you get your thyroid in high gear, you want to do everything you can to keep it there. Like Phil said, you can easily ruin your thyroid production and it can take a long time to ramp back up, assuming you do everything perfect. And there is no guarantee it will come back to 100%.