Migraine with aura: A transient cold sensation on one side of the body could be a type of aura, which is a neurological symptom that occurs before a migraine headache. This is a common condition that can cause a variety of sensory disturbances.

Trigeminal neuralgia: This condition causes sudden, severe, and brief episodes of pain, but some people may experience abnormal sensations like coldness on one side of the face.
Complex regional pain syndrome (CRPS): Although typically associated with pain, CRPS can also cause abnormal sensations such as coldness or burning in the affected limb.
Peripheral neuropathy: Damage to the peripheral nerves can cause a range of abnormal sensations, including coldness, on one side of the body.

Transient ischemic attack (TIA) or stroke: While less likely, a sudden onset of cold sensation on one side of the body could be a symptom of a TIA or stroke, especially if accompanied by other symptoms like weakness, numbness, or vision changes. Missing this diagnosis could be catastrophic.
Multiple sclerosis: This condition can cause a wide range of neurological symptoms, including abnormal sensations like coldness, and is important not to miss due to its potential for significant disability.

Sjögren's syndrome: An autoimmune disorder that can cause neuropathy and abnormal sensations, including coldness, although this would be an uncommon presentation.
Vasculitis: Inflammation of the blood vessels can cause a variety of symptoms, including abnormal sensations, but this would be a rare cause of transient cold sensation on one side of the body.
Neurosyphilis: A rare condition that can cause a range of neurological symptoms, including abnormal sensations, but is relatively uncommon in the modern era due to effective treatments for syphilis.