Are there any benefits/disadvantages/traits from having a permanent lower core temperature?

Whilst it is possible that your actual core temperature is actually lower than the normally quoted average of 37.5 Celcius by a degree, it may also be the case that where you are measuring is below the average rather than your actual core temperature. For example, you might be measuring under your armpit, and perhaps due to low circulation in that area, it does not fully reflect your actual core temperature. Just a thought. Mammalian enzymes have an optimum temperature range. Too low, and the rate of reaction is too slow to effectively support the organism. Too high, and the enzymes will denature (loose their tertiary and quaternary structure.) So if your core temperature really is a degree lower, we might expect your metabolism to be slowed due to the effect on enzyme catalysed reactions. The rule for this is expressed as Q10, Q10 temperature sensitivity units in stack biochem. Another possible effect is that a lower body temperature could mean being more prone to infection, as discussed in stack geneticsenter link description here. Temperature rise during infection (having a fever) is thought to be an attempt to thwart an infectious organism, so it follows that a lower temperature may aid teh infecting organism.