Ligamentous Sprain: Given the history of a motor vehicle accident (MVA) and the presence of knee pain, swelling, and warmth without an obvious effusion on a normal X-ray, a ligamentous sprain is a common and likely diagnosis. The lack of an obvious fracture on the X-ray and the clinical presentation point towards a soft tissue injury.

Meniscal Tear: A meniscal tear could present with pain and swelling, especially if the tear is not large enough to cause a significant effusion. The normal X-ray does not rule out a meniscal injury, as these are better visualized on MRI.
Contusion or Soft Tissue Injury: Direct trauma to the knee could result in a contusion or other soft tissue injuries, which would explain the pain, swelling, and warmth.
Patellofemoral Pain Syndrome: This condition, often related to trauma or overuse, could present with anterior knee pain and swelling, especially if the patient has been immobilized or has altered gait mechanics post-MVA.

Septic Arthritis: Although less likely without a clear source of infection or a significantly elevated fever, septic arthritis is a medical emergency that requires prompt diagnosis and treatment. The presence of warmth and swelling could be indicative of an infectious process.
Osteonecrosis: Trauma can lead to osteonecrosis, especially if there was a significant impact to the knee. Early diagnosis is crucial for treatment and prevention of further damage.
Deep Vein Thrombosis (DVT): Post-traumatic immobilization increases the risk of DVT, which can present with swelling and warmth in the affected limb. DVT is a potentially life-threatening condition if it leads to pulmonary embolism.

Spontaneous Hemarthrosis: Although rare, spontaneous hemarthrosis could occur, especially in the context of trauma. This condition involves bleeding into the joint space without an obvious source.
Complex Regional Pain Syndrome (CRPS): This is a rare condition characterized by chronic pain, inflammation, and hypersensitivity following an injury. It could be considered if the patient's pain and swelling are disproportionate to the injury and do not improve with expected treatments.
Pigmented Villonodular Synovitis (PVNS): A rare condition involving the synovial lining of the joints, PVNS could present with chronic swelling and pain. However, it is less likely in the acute setting post-MVA.