Looks like she's just using the Peltier effect to power some LEDs. I doubt the flashlights would work well, if at all, at room temperature but would be useful in a cold climate.
Well the article does say that it works ok at 41 degrees and kinda sorta at 50 degrees. As with most things, its level of impressiveness varies with your understanding of the physics involved.
The interesting question for a science fair would be to see what she had learned of the science. Did she evaluate the efficiency of the Peltier device? (typically single digit percentages) Did she compute the amount of work you could do with different energy differentials? Coming up with the total joules available, versus the joules harvested? Did she look at the efficiency of the LED to convert energy into light. What is its lumens per joule rating, and given the choices did she look at single color light (say red) versus broad spectrum light via a 'white' LED (which is a UV led exciting phosphors to get different colors). Did she go over the various enhancement strategies (drop an ice cube in a hollow tube inside the light?).
And most importantly, given what she has learned about how one can convert a temperature differential into work, what other problems might she solve with that principle?
It is unfortunate that ExtremeTech goes for the link baitey angle "ooh a flashlight that works off body heat" and less on the "Hey if we teach kids real science, they can do stuff!" (which in my opinion is a better angle on the story).
I'm not sure how it works but would having a small recess of water inside the flashlight help maintain the temperature difference? So that when you have used the flashlight enough that its temperature has risen to that of your hand, you can fill it up with water or ice and it'll cool down a little.
> " I doubt the flashlights would work well, if at all, at room temperature"
I found it a bit disappointing that they mentioned one use case as finding candles when the power is out, shortly after mentioning that it works only marginally at 50 degrees F. It takes quite a while for a normally-heated house to drop to that temperature.
It's a neat invention, no doubt, but the practical use cases for this particular version are going to be outdoors.
If the exhaust from a candle (think small, like a tea light) can be made to travel upward through the tube, and the exterior of the flashlight given sufficient heatsinking, it's possible that this arrangement can yield more visible light than the candle can produce.
I'd have to work through numbers to guess, and do the experiment to be sure...