Heat Stroke: This is the most likely diagnosis for hyperpyrexia, especially in the context of high environmental temperatures or strenuous physical activity. Heat stroke occurs when the body's temperature regulation fails, causing a rapid rise in body temperature, often above 40°C (104°F). It is characterized by altered mental status and can be life-threatening if not promptly treated.

Meningitis: Infections such as meningitis can cause high fever, which may present as hyperpyrexia. Meningitis is an inflammation of the protective membranes covering the brain and spinal cord, known as the meninges. This condition is medical emergency.
Sepsis: Sepsis, a life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs, can also lead to hyperpyrexia. The body's temperature regulation can be severely disrupted in sepsis.
Neuroleptic Malignant Syndrome (NMS): NMS is a rare but life-threatening side effect of neuroleptic or antipsychotic drugs. It is characterized by fever, muscle stiffness, and altered mental status, which can include hyperpyrexia.
Serotonin Syndrome: This is a potentially life-threatening medical condition resulting from an excess of serotonin in the central nervous system. Symptoms can include high body temperature, among others, and it is often associated with the use of certain medications.

Thyroid Storm: A life-threatening complication of untreated or undertreated hyperthyroidism, characterized by an extreme exacerbation of thyrotoxicosis symptoms, including very high fever. Although less common, missing this diagnosis can be fatal.
Pheochromocytoma: A rare tumor of the adrenal gland that can cause episodes of high blood pressure, fever, and other symptoms due to the excessive release of catecholamines. While rare, it is critical not to miss this diagnosis due to its potential for severe complications.
Drug Fever: Certain medications can induce fever without any identifiable source of infection, which can sometimes present as hyperpyrexia. Identifying and stopping the offending drug is crucial.

Diencephalic Epilepsy: A rare condition that affects the diencephalon, the part of the brain that includes the thalamus, hypothalamus, epithalamus, and subthalamus. It can cause periodic hyperthermia among other symptoms.
Familial Dysautonomia (Riley-Day Syndrome): A rare genetic disorder that affects the development of the autonomic nervous system, leading to various symptoms including episodes of hyperpyrexia.
Cytokine Release Syndrome: A systemic inflammatory response that can occur after certain immunotherapies, characterized by high fever, among other symptoms. While more recognized in specific contexts, it remains a rare cause of hyperpyrexia in the general population.