High blood pressure is a problem for hyperthyroid and hypothyroid patients. In hypothyroidism, noradrenaline is secreted to compensate for the lack of thyroid hormone, and this causes not only high blood pressure, but a fast heart rate, anxiety, and other symptoms. The diastolic (lower) number is often higher than 90 mm Hg. Bringing thyroid levels up will often normalize blood pressure. I profiled my experience with the condition here: Hyperthyroid Symptoms (Anxiety, Tachycardia); Hypothyroid Labs
In hyperthyroidism, T3 reduces systemic vascular resistance (resistance to blood flow), heart rate elevates, and cardiac output increases; these all raise blood pressure. The systolic (upper) number is often higher than 140 mm Hg. Pulse pressure refers to the difference between the systolic (upper) and diastolic (lower) numbers. A widened pulse pressure is a common feature in hyperthyroidism. Long-term negative effects on the cardiovascular system include arterial stiffness and left ventricular hypertrophy (thickening of the heart muscle).
If you are taking T3 in any form (desiccated thyroid or liothyronine like Cytomel), and your systolic BP is over 140 mm Hg while your diastolic number is less than 90 mm Hg, you may need to adjust/reduce your dose. A resting heart rate over 85 beats per minute also suggests overmedication, as does any form of arrhythmia (irregular heartbeat, especially atrial fibrillation).
If your diastolic BP is over 90 mm Hg and you have a high heart rate and anxiety, along with other symptoms of hypothyroidism like dry skin, brain fog, and a body temperature that never reaches 98 oF, then your dose may be too low, and you should certainly get more complete testing that includes a Free T3. http://tiredthyroid.com/what-labs.html
 Streeten, D. H., et al. “Effects of thyroid function on blood pressure. Recognition of hypothyroid hypertension.” Hypertension 11.1 (1988): 78-83.
 Prisant, L. Michael, Jaspal S. Gujral, and Anthony L. Mulloy. “Hyperthyroidism: a secondary cause of isolated systolic hypertension.” The Journal of Clinical Hypertension 8.8 (2006): 596-599.