Mechanically there are a few different implications of this, one is that we already have an adjustment factor in place to the homeostasis code that assumes you’re being fairly active. The main difference when tracking it directly is that when inactive, people are going to get much colder much faster (except when asleep, we already suppress heat generation when asleep), and occasionally (extended manual labor or fighting) will get much warmer, so it will increase the dynamic range of body temperature and your need to manage it.
After living in a cold environment and exercising frequently outside, I have to point out another issue with sweat, if it’s cold enough that you still wear layers of clothes even when exerting yourself, you start getting sweat buildup inside your clothes, which puts you in a pickle if you stop exerting yourself, because your body temperature will absolutely plummet when you stop moving.
These are the effects, I pretty much have how the implementation would work sorted out, it’s mostly a matter of tagging all the places where the player takes action with a call to record how much they’re exerting themselves, probably in a small range of values like “idle”, “moving”, “exerting”, “sprinting” to keep things simple, then updating the body temperature code to take that value into account.