According to a single study released less than a year ago.
I just read the study, and it seems they measured "body temperature" via sensors in the abdominal cavity. That's pretty weak because exercise-induced hyperthermia starts in the working muscles. I don't see any reason to expect an increase in core temperature within 40 seconds or so of a cheetah starting to sprint.
But, having sprinted in hot weather many times myself, I do expect to see a sustained increase in core temperature after a 40-second sprint, just as the study found for cheetahs. It also found that the temperature increase was greater for cheetahs after successful hunts than aborted ones, just as I sweat more after a complete all-out rep than if I step off the track early. And while the successfully-hunting cheetahs didn't usually end up with core temperature above 40.5C, their average increase was a significant 1.3C, and it would make sense for them to leave a margin of safety so they can combat or escape from competitors after the kill.
So it seems more likely to me that the cheetahs abort most of their hunts because they either would be dangerously close to overheating afterward if they continued, or because the resulting sustained core temperature increase would interfere with second attempts for the next hour or two. I also have little doubt that a cheetah that attempted to sprint indefinitely would fare differently than the cheetahs studied which did not.
Whether the hyperthermia is exercise-induced or not, they propose no mechanism or evidence supporting stress-induced hyperthermia. All they've got is
which is at best evidence that a cheetah can get warmed up by means other than a sprint, and that a cheetah can suffer stress, not that stress hyperthermia is actually occurring. They are speculating.
http://royalsocietypublishing.org/content/9/5/20130472