Thyroid cancer and heredity? How much does heredity play a part in getting thyroid cancer? Is it different if the relative who had it is a cousin vs. A mother or an aunt? What about an identical twin?

A little bit. Authorities think about 5% of patients with thyroid cancer may have a hereditary component. We can't identify the genes yet, and go by "clusters. In general, the closer the relative, the more likely you will have thyroid cancer, assuming that this has an hereditary component. But most dont.
There . There are several types of thyroid cancer. The most common ones are papillary and follicular. There is a slight hereditary link with these cancers. Medullary throid cancer (third and fairly rare type) has a stronger hereditary link--up to 20% of people with this cancer have an abnormal gene, and there are some genetic syndromes that also have medullary cancer as a characteristic. The hereditary risk is highest with a first degree relative (parent, sibling, or child).