Not sure about the turning it way up and running around naked, but the core idea is pretty solid. It’s why gyms that want to do things right run cold, making your body do just a big more work (gyms that want you to feel good run hot, making you sweat faster). Because for most of us weight is a matter of just a couple of calories here for there (the 2 pounds a year Americans gain on average equates to about 75 calories a day) small changes can have pretty significant effects. Even if all you do is burn an “extra” 2 calories per resting hour, that’s 2/3 of the average American’s overage.
Except the body will simply want to consume more calories to account for the extra ‘burn’. The ONLY way this would work is if the caloric consumption remained static.