**Core Concept**
The patient is presenting with symptoms of hyperthyroidism, including weight loss, palpitations, and warm moist skin, in the context of undetectable TSH and normal free T4 levels. This suggests a case of TSH receptor antibody-mediated hyperthyroidism, such as Graves' disease.

**Why the Correct Answer is Right**
Given the clinical presentation and laboratory findings, the next best step is to perform a radioactive iodine uptake (RAIU) scan to evaluate the thyroid gland's ability to take up iodine. This test can help differentiate between various causes of hyperthyroidism, including Graves' disease, toxic nodular goiter, and thyroiditis. The RAIU scan is particularly useful in this case, as the normal free T4 levels and undetectable TSH suggest a euthyroid state, but the clinical symptoms point towards hyperthyroidism.

**Why Each Wrong Option is Incorrect**
**Option A:** A computed tomography (CT) scan of the thyroid gland might be useful in evaluating thyroid nodules or masses, but it is not the next best step in diagnosing hyperthyroidism.

**Option B:** A thyroid-stimulating hormone (TSH) receptor antibody test can help confirm the diagnosis of Graves' disease, but it is not the next best step in the diagnostic algorithm.

**Option C:** A free T4 and free T3 (FT4 and FT3) level can provide more information about the patient's thyroid hormone status, but the normal free T4 level already suggests euthyroidism.

**Clinical Pearl / High-Yield Fact**
In cases of suspected hyperthyroidism, it is essential to consider the possibility of TSH receptor antibody-mediated disease, such as Graves' disease, which can lead to destructive thyroiditis or thyroid neoplasia if left untreated.

**Correct Answer:** C.