Measurement of the serum free thyroxine (T₄) level is the most appropriate next step in management for this patient who has clinical evidence of hypothyroidism (fatigue, constipation, cold intolerance, dry skin, delayed reflexes, anemia, and mild hyponatremia) but has had radiation to the base of the skull, including the pituitary gland. Although measurement of thyroid-stimulating hormone (TSH) is the most accurate reflection of thyroid status in patients with an intact hypothalamic-pituitary-thyroid axis, it is not a reliable measure of thyroid function in patients in whom there is loss of hypothalamic-pituitary function, such as seen in this patient. His low-normal TSH in the context of clinical hypothyroidism suggests possible central hypothyroidism, and measurement of the circulating level of thyroid hormone, the free serum T₄, would therefore be a more accurate indication of his thyroid status.

Repeating the TSH measurement would not be appropriate in this patient with signs and symptoms of hypothyroidism, as untreated hypothyroidism leads to increased cardiovascular morbidity and mortality. In addition, because of likely central hypothyroidism, the TSH level would remain an inaccurate indicator of thyroid function.

Thyroid scintigraphy is unlikely to distinguish the source of the hypothyroidism, as patients with primary or secondary hypothyroidism have decreased radioactive uptake. Thyroid scanning is most helpful in elucidating the cause of hyperthyroidism.

Ultrasound of the neck is normal in patients with central hypothyroidism and would be unlikely to provide any additional information about this patient's thyroid status.