There is good reason to believe that levels of thyroid hormones, and the changes in thyroid function they represent, influence human longevity. These are amongst a number of hormones in the human body that touch on almost everything you would expect to influence life span over time: metabolic rate, cell growth, use and processing of food, and so forth. You might recall studies on the thyroid hormone triiodothyronine, or T3, for example:
The hypothalamo-pituitary-thyroid axis has been widely implicated in modulating the aging process. Life extension effects associated with low thyroid hormone levels have been reported in multiple animal models. In human populations, an association was observed between low thyroid function and longevity at old age ... These findings suggest that the favorable role of low thyroid hormone metabolism on health and longevity in model organism is applicable to humans as well.
Here is another, more recent study of a human population that pulls in more confirming data:
The objective of the study was to test whether low thyroid activity associated with extreme longevity constitutes a heritable phenotype, which could contribute to the familial longevity observed in the Leiden Longevity Study. ... Eight hundred fifty-nine nonagenarian siblings (median age 92.9 yr) from 421 long-lived families participated in the study. Families were recruited from the entire Dutch population if at least two long-lived siblings were alive and fulfilled the age criterion of age of 89 yr or older for males and 91 yr or older for females.
We found that a lower family mortality history score (less mortality) of the parents of nonagenarian siblings was associated with higher serum TSH levels (P = 0.005) and lower free T4 levels (P = 0.002) as well as lower free T3 levels (P = 0.034) in the nonagenarian siblings. ... Our findings support the previous observation that low thyroid activity in humans constitutes a heritable phenotype that contributes to exceptional familial longevity observed in the Leiden Longevity Study.
This matter of thyroid hormones is largely an inherited factor in your biochemistry, but it is worth noting that the practice of calorie restriction (CR) is shown to reduce T3 levels - and there is every reason to expect this to be beneficial:
Long-term CR with adequate protein and micronutrient intake in lean and weight-stable healthy humans is associated with a sustained reduction in serum T3 concentration, similar to that found in CR rodents and monkeys. This effect is likely due to CR itself, rather than to a decrease in body fat mass, and could be involved in slowing the rate of aging.
Rozing MP, Houwing-Duistermaat JJ, Slagboom PE, Beekman M, Frölich M, de Craen AJ, Westendorp RG, & van Heemst D (2010). Familial Longevity Is Associated with Decreased Thyroid Function. The Journal of clinical endocrinology and metabolism PMID: 20739380