Menopause-related symptoms: Given the patient's age and the description of feeling "hot," this could be related to menopausal hot flashes, which can sometimes be accompanied by a burning sensation. However, the fact that it's been ongoing for 2 years and specifically occurs at night might suggest other underlying causes as well.

Trigeminal Neuralgia: This condition can cause intense, burning, or electric shock-like pain in parts of the face, which might radiate to the shoulders and could be worse at night. However, it typically involves one side of the face.
Cervicogenic Headache: Pain from the cervical spine can refer to the head and might be described as a burning sensation, especially if there's involvement of the cervical nerves.
Fibromyalgia: Characterized by widespread musculoskeletal pain accompanied by fatigue, sleep, memory, and mood issues. The burning sensation could be part of the symptom complex, especially if it worsens at night.
Medication Side Effects: Certain medications can cause a burning sensation as a side effect, which could be exacerbated at night.

Multiple Myeloma: Although rare, this condition can cause a range of symptoms including bone pain, which might be described as a burning sensation, especially if there are lesions in the skull or spine.
Thyroid Disorders: Both hyperthyroidism and hypothyroidism can cause a variety of symptoms including heat intolerance or sensitivity, which might be perceived as a burning sensation.
Vitamin Deficiencies (B12, etc.): Deficiencies in certain vitamins can lead to neurological symptoms, including burning sensations in the extremities or head.
Temporal Arteritis: An inflammatory condition affecting the blood vessels, particularly those in the head, which can cause severe headaches and other symptoms. It's crucial to diagnose early to prevent complications like vision loss.

Complex Regional Pain Syndrome (CRPS): A condition characterized by burning pain, typically in an arm or leg, after an injury or trauma. It's less common for CRPS to present primarily in the head and shoulders.
Erythromelalgia: A disorder characterized by burning pain, heat, and redness in the hands and feet, but it can rarely affect other areas, including the head and shoulders.
Neoplastic Processes: Rarely, a burning sensation could be the presenting symptom of a tumor affecting the nerves or spinal cord, such as a schwannoma or meningioma.