Treatment of thyroid cancer depends on the type of cancer. Most thyroid cancers are inciduous onset and have qeustionable influence on mortality. However, the consensus by far in the majority of cases is to remove the thyroid gland completely without damaging the critical structures nearby. Again, depending on the type of cancer and the degree of spread potential or lymph node involvement, most patients will receing a dose of radioactive iodine with the intent to "mop up" any residual thyroid tissue left behind during surgery. There is considerable controversy whether this actually "destroys" possible residual cancer since the dose is much lower than would be needed to kill cancer. The point of this dose is merely to clear the field to provide better ability to monitor. Monitoring consists of routine ultrasounds of the neck to examine recurrence in lymph nodes or the surgical field, and surveillance measurement of thyroid-specific proteins in the blood (thyroglobulin), which in theory should no longer be detectable.
Again, depending on the type of cancer and the patient's age and other risks, and additional treatment recommendation is to use "suppressive" doses of thyroid hormone with the intent of slighlty over-replacing the amount of thyroid hormone the body would typically require in order to suppress any residual thyroid tissue (or cancer) from being stimulated to grow.
The pituitary gland secretes a hormone called TSH which is the main stimulus for the thyroid to make thyroid hormone. The hypothalamus secretes a hormone called TRH (thyrotropin releasing hormone) whose job it is to tell the pituitary gland to release TSH. The hypothalamus assesses whether there is sufficient thyroid hormone circulating in the blood. If it detects there is too little then it tells the pituitary which in turn tells the thyroid to make more. In the case of patients who now do not have a thyroid gland, the whole process is dependent on taking the correct dose of thyroid hormone as a pill. TRH is almost impossible to measure in the blood stream with out very sophisticated research techniques (remember, it is only telling the neigboring pituitary gland what to do and thus TRH can not be found in the circulating blood stream). TRH does not exist as a drug. Even if it could be produced, for the above reasons it would have no net benefit since the end effect is to tell the thyroid to make more hormone (and the thyroid is gone in this case).