Here is a very brief high level overview of some of what is known about the relationship between body temperature and longevity in mammals. As for many aspects of our biology, researchers have pulled out associations from the data but questions of cause, effect, and mechanisms involved are all very much up for debate.
Some studies show a correlation between lower body temperatures and greater longevity, though there is no proof of a cause-and-effect relationship in humans. The first such major study in warmblooded animals was a 2006 experiment involving mice at the Scripps Research Institute. Genetically engineered mice with extra-sensitive temperature control switches in the hypothalamus were raised with core body temperatures just a fraction of a degree cooler than those of their litter mates; caloric intake was the same. The researchers found the median life span was 12 percent greater in the cooler males, 20 percent greater in the females.
As for humans, a large study published in 2011 compared the ages and body temperatures of 18,630 people from 20 to 98 years old who had oral temperature readings as part of a standardized health appraisal at a health maintenance organization. Mean temperature decreased with age, with a difference of 0.3 degrees Fahrenheit between the oldest and youngest groups, even after controlling for sex, body mass index and white-blood-cell count.
"The results are consistent with low body temperature as a biomarker for longevity," the researchers concluded. As for possible reasons for such results, they suggested identifying genetic influences on body temperature and examining the effect of body temperature on multiple cellular processes.