I don't think the rear projection TVs have Fresnel lenses.
https://en.m.wikipedia.org/wiki/Fresnel_lens
Inside there's three lens setups & if you are taking the Cast Ali end off, beware, there's a lot of a thin clear oil inside it. You can pop the rubber bubble to drain most of it out first.
The front plastic clear screen has a texture to it that's similar to a Fresnel lens, but it's just vertical lines made to concentrate & then spread the individual pixel spots.
I think the confusion comes from a 1960's -70's gimmick you could buy, it's a big sheet plastic Fresnel lens which you could mount in front of a smaller TV 14 - 21 inch screen, and it would magnify it up to 26-29 inches.
It was only good if you were directly in front of it & didn't mind a colourful aurora thru the picture ( that probably didn't matter much in the late '60's, maybe it even helped...)
I have seen a much smaller A4 size version sold as a 'Vehicle rear window reversing lens'.
And yes, they will heat up something extremely fast with just sunlight, even if it's unfocused.
At the same time, those lenses in the rear projection screen TVs. I left one on my passenger seat during the day.
When I shifted it I found a thin arc of burn marks across the seat, right thru the material.
You can actually see the sun's movement thru the whole day & where it was brighter & overcast as the sun moved thru it's arc.
I'm lucky it didn't catch on fire.
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