I have hypothyroidism, i've had my thyroid removed, im 39 & doctor put me on corticosteroids for temporal arteritis, will this worsen hypothyroidism ?

No: Sometimes the TSH can be low when on steroid but if the thyroid hormone levels like T4 and T3 (liothyronine) are measured they are usually in the normal range so a change in dose is not typically required.

Possibly: Steroids can affect the thyroid, so if they are something you are going to be on very long, i would check with your endocrinologist or whoever is monitoring your hypothyroidism...