**Core Concept**
The patient's presentation of low-grade fever and bilateral hilar adenopathy with clear lung fields is suggestive of sarcoidosis, a systemic granulomatous disease characterized by the accumulation of non-caseating granulomas in various organs, particularly the lungs and lymph nodes.

**Why the Correct Answer is Right**
Sarcoidosis is often diagnosed based on clinical findings, imaging studies, and laboratory tests. In this case, bilateral hilar adenopathy with clear lung fields is a classic radiographic finding in sarcoidosis. The patient's low-grade fever may be related to the systemic inflammation and granulomatous reaction. The utility of various investigations in making the diagnosis can be evaluated based on their ability to confirm or exclude sarcoidosis.

**Why Each Wrong Option is Incorrect**
**Option A:** Angiotensin-converting enzyme (ACE) levels are often elevated in sarcoidosis and can be used as a supportive diagnostic marker. Therefore, measuring ACE levels can be useful in making the diagnosis.

**Option B:** Gallium-67 scans can be used to identify areas of inflammation and granulomatous disease, which are characteristic of sarcoidosis. Thus, gallium-67 scans can be useful in making the diagnosis.

**Option C:** Pulmonary function tests (PFTs) can show restrictive lung disease or interstitial lung disease in patients with sarcoidosis. Therefore, PFTs can be useful in assessing the extent of pulmonary involvement in sarcoidosis.

**Option D:** Although serum calcium levels may be elevated in sarcoidosis due to vitamin D activation by macrophages within granulomas, this is not a specific or sensitive test for the diagnosis of sarcoidosis. It can, however, be a useful marker to monitor for hypercalcemia of malignancy.

**Clinical Pearl / High-Yield Fact**
In sarcoidosis, the presence of bilateral hilar adenopathy with clear lung fields is a classic radiographic finding. This pattern is often seen in the early stages of the disease.

**Correct Answer:** D. Serum calcium levels are not a specific or sensitive test for the diagnosis of sarcoidosis, but can be useful to monitor for hypercalcemia of malignancy.