Thyroid hormones have a direct effect on most organs, including the heart, which beats faster and harder under the influence of increased thyroid hormones (this is why heart problems can often accompany chronic thyroid problems in women, and perhaps why heart problems are more common in women under the age of 50).
T3 is the more biologically active hormone. It's more important for cellular function, and in fact, 80% of T4 is converted to T3 in the body's peripheral tissues. Basically, T4 is just a precursor for the more active hormone, T3.
One of the problems in some thyroid disorders is that you may have trouble converting T4 to T3 in your tissues. Have you been checked for this? This can create a deficiency of T3, disrupting the body's ability to properly regulate metabolism, which leads to specific symptoms.
There are some clinicians that are supporting thyroid conditions with iodine. I do not recommend iodine in supporting thyroid conditions. According to renowned thyroid expert Dr. Datis Kharriazian, author of the book "Why Do I Still Have Thyroid Symptoms?", using iodine to support thyroid conditions is like throwing gasoline on a fire.