How do changes in temperature affect body weight in humans?
You would see moderate weight gain in both subjects.

Since humans thermoregulate and aren't terribly "adapted" to any extreme for either very hot or very cold climates, anything outside of short range of temperatures will cause us to either sweat or shiver.

Sweating or shivering will cost kcals ("Calories", "Joules"), and the extra energy expenditure will keep the subjects' weights lower than they would otherwise be.

Once the subjects enter an environment where they no longer need to sweat, shiver, or basically maintain a wide gap between the outside temperature and their body temperatures (which is the real driver here - the difference between the two), they will no longer expend as much energy maintaining human body temperature.

How much energy are they saving? Not much. I wish I could find the article again, but you're talking an extra 50kcal or so an hour saved - or a few pounds until the energy required to maintain the extra weight reaches equilibrium with the energy saved.

There are a few assumptions built into the above, which sees the question as more of a physics-oriented hypothetical than real-world example. In reality you have some large complications - getting anything done in cold temperatures is going to require a much larger energy expenditure, as you're usually carrying 30-50lbs of gear to not freeze to death, for example. A person used to wearing a dozen kilograms of animal furs during their weekly routine would gain a lot more weight than hypothesized above if they suddenly entered a mild climate with similar food intake, but without the constant load on their muscles.