I have the zagg glass screen protector, and yes sometimes when I pull the SP3 out of the sleeve it's hot. I figured that the way I was putting the SP3 in the sleeve caused it to turn on whenever there was a bump, to solve it by adjusting the way I stored the unit in the sleeve.
The screen protector is solid, bought it at best buy and no signs of it slipping off.
Is the zagg glass protector also 0.5mm or is it thinner than Microsoft's? Either way, I ended up getting a matte screen protector from Future Shop (didn't know this, but they have generic ones, matte and glossy), that they apply in-store. Not glass or anything, but thin enough that I can still put on my folio-case without it shifting the protector around and lifting the edges. Better protection overall I think than going naked apart from the glass screen protector.
Took around 20 minutes to install and came with lifetime replacement warranty which was nice.