Piriformis Syndrome: This condition is characterized by pain in the posterior thigh and heel due to compression of the sciatic nerve by the piriformis muscle. The improvement of pain with movement and worsening with sitting is consistent with this diagnosis, as sitting can increase pressure on the sciatic nerve.

Hamstring Strain: Although the patient reports no known precipitating injury, a mild strain could cause intermittent pain in the posterior thigh. The pain pattern of improving with movement and worsening with sitting could fit if the strain is mild and movement helps reduce muscle spasm.
Sciatica: This is a common condition causing pain in the lower back, posterior thigh, and heel due to irritation of the sciatic nerve. The symptoms can be exacerbated by sitting and relieved by movement, depending on the underlying cause of the sciatica.

Deep Vein Thrombosis (DVT): Although less likely given the description, DVT can cause pain in the thigh and can be exacerbated by sitting due to increased venous pressure. It's crucial to consider DVT due to its potential for severe complications, such as pulmonary embolism.
Cauda Equina Syndrome: A rare but serious condition where the nerves in the spinal canal are compressed, leading to pain, numbness, and potentially severe neurological deficits. Early recognition is critical to prevent long-term damage.

Peripheral Artery Disease (PAD): This condition involves narrowing of the arteries, which can lead to pain in the legs upon exertion (intermittent claudication) and relief with rest. However, the pattern described (improvement with movement and worsening with sitting) is less typical for PAD.
Tumors (e.g., Soft Tissue Sarcomas): Although extremely rare, tumors in the posterior thigh could cause pain. The absence of a mass or other systemic symptoms makes this less likely, but it remains a consideration in the differential diagnosis due to its potential severity.