I love Penn and Teller. This clip was highly amusing. It's essentially the placebo effect. People do the same stuff with wine tasting too. Tell them it's a $3 bottle, and they'll tell you it's cheap garbage. Tell them it's a $30 bottle, and they'll say it's pretty good. Tell them it's a $300 bottle, and they'll consult a thesaurus or just make up new words.
Diet has changed substantially. People eat a hell of a lot more than they did 100 years ago.
The difference in the amount of calories that you burn in the heat vs in cooler temperatures is minimal. I have read though, that constant exposure to extreme heat will increase your base metabolic rate by around 5-20%. Of course, if you go running in 100 degrees, you'll likely get heat stroke unless you're conditioned for it. With heat stroke, may come nausea and vomiting. You'll likely have less appetite as well. Ohh, and you could also go into a coma and even die too.
Now, even at rest, if you go into the extreme cold, your body will burn more calories since it has to work to generate heat. Thus, I propose, buy yourself a walk in freezer, set it to 0f, and live in it.