Ask for NON-ionic contrast (administered via IV, it seems to have lesser effects.
the best option is to use technetium contrast media.
Excerpt from Australian Prescriber - Safe use of radiographic contrast media...
"Iodinated contrast-induced thyrotoxicosis is rare. Iodine does not have a significant effect on patients with normal thyroid function. Patients with Graves' disease and multi nodular goitre are at increased risk, and those with thyrotoxicosis should not receive the contrast.
Patients with hyperthyroidism may develop a thyroid crisis and the accuracy of thyroid function tests will be affected by intravascular contrast media. These contrast media can also affect diagnostic thyroid isotope studies for up to eight weeks. Patients with thyroid carcinoma scheduled for treatment with radioactive iodine should not receive the contrast, as it may delay treatment for eight weeks."