The thyroid, the largest gland in the endocrine system, secretes hormones that help promote bodily growth and development. This gland regulates hormonal secretion rate in spite of changes in dietary iodine which is a key ingredient in the hormone's biosynthesis. The thyroid relies on several feedback mechanisms for this regulation, and in this paper we use recent molecular-level and clinical observations to engineer a computational thyroid model. We use simulation and analysis to show that this models captures known aspects of thyroid physiology. We identify features in the model that are responsible for hormonal regulation, and use the model to identify and evaluate competing hypotheses associated with Wolff-Chaikoff escape.