Being thorough: "The proposition that increased energy expenditure shortens life has a long history. The rate-of-living theory states that life span and average mass-specific metabolic rate are inversely proportional. Originally based on interspecific allometric comparisons between species of mammals, the theory was later rejected on the basis of comparisons between taxa (e.g., birds have higher metabolic rates than mammals of the same size and yet live longer). It has rarely been experimentally tested within species. Here, we investigated the effects of increased energy expenditure, induced by cold exposure, on longevity in mice. Longevity was measured in groups of 60 male mice maintained at either 22 degrees C (WW) or 10 degrees C (CC) throughout adult life. ... we observed no significant differences in median life span among the groups ... [energy expenditure] in CC mice significantly exceeded that of WW mice. This result demonstrates that increased energy expenditure does not shorten life span and adds evidence to the intraspecific refutation of the rate-of-living theory."

Link: http://www.ncbi.nlm.nih.gov/pubmed/19115965