Cheetah (Acinonyx jubatus) are the fastest mammals, and use “stalk and chase” hunting. Anomalously, they abandon more than half of their chases when prey ought to be in range, and both successful and unsuccessful hunts are followed by periods of inactivity. The entrenched explanation is that cheetah abandon hunts because they overheat. That explanation can be traced to a single study, in which Taylor and Rowntree (1973) ran two hand-reared cheetah on a treadmill, and concluded that cheetah stored metabolic heat to the extent that further exercise soon became impossibly thermally. They predicted that cheetah would not run when body temperature reached 40.5°C. We used biologgers to measure core body temperature (abdominal cavity) and locomotor activity (subcutaneous, hind leg) of four cheetah, living free, and hunting, in a conservancy in Namibia. For implantation, the cheetah were immobilized and anaesthetized with medetomidine (0.023±0.002mg.kg-1, mean±SD) and zoletil (1.5±0.2mg.kg-1) intramuscularly, via capture dart, and intubated; anaesthesia was maintained under spontaneous breathing with 2-4% halothane in oxygen. After recovery, the cheetah were released into the conservancy. We observed both successful (12±3 per cheetah) and unsuccessful (6±2 per cheetah) hunts. We found that the cheetah abandoned many hunts but not because they overheated. Indeed, core body temperature only rarely exceeded 40.5°C, and did not rise significantly during a chase. The abdominal temperature at which unsuccessful hunts were abandoned was 38.3±0.2°C. Abdominal temperature did rise gradually after the chase, for 44±17min after successful hunts. The temperature increase (1.3±0.2°C vs. 0.5±0.1°C, 0.0001<P<0.04, unpaired t tests on each cheetah) and the area under the temperature increase/time curve (78±19°C.min vs. 9±8°C.min, 0.0004<P<0.04, unpaired t tests on each cheetah) were significantly higher after successful hunts than after unsuccessful hunts, despite there being no difference in activity between successful and unsuccessful hunts. A similar increase in core body temperature was evident in one cheetah that participated in a feed after a successful hunt by siblings, but was not directly involved in the hunt. We propose that the increased body temperature relates to sympathetic activation, greater following successful than unsuccessful hunts. Why cheetahs abandon a chase when the prey ought to be in range therefore remains unknown.