Fever and anapyrexia are the most studied thermoregulatory responses. They are defined as a body temperature (T(b)) increase and decrease, respectively, occurring because of a shift in the set point (SP) and characterized by active defense of the new T(b). Although models of T(b) control with a single SP (whether obvious or hidden) have been criticized, the SP-based definitions have remained unchallenged. In this article, the SP-based definitions of fever and anapyrexia were subjected to two tests. In test 1, they were compared with experimental data on changes in thresholds for activation of different thermoeffectors. Changes in thresholds were found compatible with an SP increase in some (but not all) cases of fever. In all cases of what is called anapyrexia, its mechanism (dissociation of thresholds of different effectors) was found incompatible with a decrease in a single SP. In test 2, experimental data on the dependence of T(b) on ambient temperature (T(a)) were analyzed. It was found that the febrile level of T(b) is defended in some (but not all) cases. However, strong dependence on T(a) was found in all cases of anapyrexia, which agrees with threshold dissociation but not with a decrease of the SP. It is concluded that fever (as defined) has only limited experimental support, whereas anapyrexia (as defined) does not exist. Two solutions are offered. A palliative is to accept that SP-based terms (anapyrexia, cryexia, regulated hypothermia, and such) are inadequate and should be abandoned. A radical solution is to transform all definitions based on comparing T(b) with the SP into definitions based on balancing active and passive processes of T(b) control.