In a way, it depends on how we define mental effort. If you concentrate on raising your heart and breathing rates - which are physical, but then so in a sense is mental effort - you can significantly affect calorie burn.
Right, and if you decide to run a marathon or become an Olympic athlete, that mental effort is going to burn even more calories. So I think it's clear that they're talking about calories burned by the mental activity, not calories burned by physical activity that was the result of mental activity.
I don't think that's what he meant. There is some evidence that with training some people can raise their heart rate or body temperature purely by thinking about it.
I had one girlfriend who became like a furnace when she slept. She slept with no covers with the window open in January in Ohio. I had to strip down to just one sheet. Literally, it was like sleeping next to a space heater. So it is possible for the body to increase its metabolic rate.
For the purposes of temperature control in places with extremely tight environmental requirements, the modelling assumption is that a human being gives off the same amount of thermal energy as a standard 100-watt incandescent lightbulb. When you check into the clean room, you turn off your bulb. When you leave you turn it back on. The bulbs also serve as a handy way to tell who is in the lab that day :)
I didn't realize that, and while it's informative and interesting, that doesn't change the issue: the article was talking about the extra calorie consumption from the mental process, not the extra calorie consumption caused by a mental process that leads to raising one's pulse, flexing one's abs, moving one's eyes, typing a comment, or swimming a lap.