Is there a homebrew temperature measuring tool? Fairly simple to test these things if so.
I would probably be more concerned about it emitting interference and receiving it. Looking at steps 5 and 6 of
https://www.ifixit.com/Teardown/Nintendo+Switch+Teardown/78263 then it is covered in small holes. That is an extra step (extra steps cost, cost an awful lot when you are making millions of the things), does little for cooling, will not do much for weight reduction, won't do much for strength compared to all the other features of that stamping and thus we are back to EM, if you want a nice technical article then
https://www.electronic.nu/2017/02/08/shielding-of-boxes-and-enclosures-part-2/
On the matter of cooling it is thermally coupled it seems but there is not a great deal of thermal mass there.
Seems someone did point a thermal camera at it in game (looks like Zelda)
Not seeing a lot of heat outside of where I would expect or what I would expect to see if it were aiming to act as a radiator.
Structure wise I imagine/hope a clear case will be some nice polycarbonate which should take care of some of the strength/rigidity concerns -- as long as you don't get acetone on it polycarbonate is very tough (there is a reason it is used for riot shields and face masks), but is also expensive. If you are paying up for a fancy shell then no worries there about cost.
After this I am contemplating nonsense like what if the battery went pop. Said sheet would not do much beyond turn a very bad day into still a very bad day but not quite as much as before.
Also if you fancy sharing some pictures I would not mind seeing some. I don't know expect to see cosmetic replacement cases like this at this point in the game.