These are:
Quotidian fever, with a 24-hour periodicity, typical of malaria caused by Plasmodium knowlesi (P. knowlesi);
Tertian fever, with a 48-hour periodicity, typical of later course malaria caused by P. falciparum, P. vivax, or P. ovale;
Quartan fever, with a 72-hour periodicity, typical of later course malaria caused by P. malariae.In addition, there is disagreement regarding whether a specific fever pattern is associated with Hodgkins lymphoma—the Pel–Ebstein fever, with patients argued to present high temperature for one week, followed by low for the next week, and so on, where the generality of this pattern is debated.Persistent fever that cannot be explained after repeated routine clinical inquiries is called fever of unknown origin. A neutropenic fever, also called febrile neutropenia, is a fever in the absence of normal immune system function. Because of the lack of infection-fighting neutrophils, a bacterial infection can spread rapidly; this fever is, therefore, usually considered to require urgent medical attention. This kind of fever is more commonly seen in people receiving immune-suppressing chemotherapy than in apparently healthy people. Hyperpyrexia
Hyperpyrexia is an extreme elevation of body temperature which, depending upon the source, is classified as a core body temperature greater than or equal to 40 or 41 °C (104 or 106 °F); the range of hyperpyrexias includes cases considered severe (≥ 40 °C) and extreme (≥ 42 °C). It differs from hyperthermia in that ones thermoregulatory systems set point for body temperature is set above normal, then heat is generated to achieve it.
Other species
Fever is an important metric for the diagnosis of disease in domestic animals. The body temperature of animals, which is taken rectally, is different from one species to another. For example, a horse is said to have a fever above 101 °F (38.3 °C). In species that allow the body to have a wide range of "normal" temperatures, such as camels, whose body temperature varies as the environmental temperature varies, the body temperature which constitutes a febrile state differs depending on the environmental temperature. Fever can also be behaviorally induced by invertebrates that do not have immune-system based fever. For instance, some species of grasshopper will thermoregulate to achieve body temperatures that are 2–5 °C higher than normal in order to inhibit the growth of fungal pathogens such as Beauveria bassiana and Metarhizium acridum. Honeybee colonies are also able to induce a fever in response to a fungal parasite Ascosphaera apis. References
Further reading
Rhoades R, Pflanzer RG (1996). "Chapter 27: Regulation of Body Temperature (Clinical Focus: Pathogenesis of Fever)". Human Physiology (3rd ed.). Philadelphia, PA: Saunders College. ISBN 9780030051593. Retrieved 2 April 2020. External links

Fever and Taking Your Childs Temperature
US National Institute of Health factsheet
Drugs most commonly associated with the adverse event Pyrexia (Fever) as reported the FDA
Fever at MedlinePlus
Why are We So Afraid of Fevers? at The New York Times