Smells very like a duff capacitor somewhere given the behaviour you describe. Don't think the screen itself is at fault and probably not the ribbon working loose.
This one is a standalone 15" Dell which you're welcome to if you want it.
As above I'd pop the big board off and flip it over, inspect all the capacitors. Change out any which are bulging on the sides or the end.
Here's a video card I have in my drawer which also has screen artifacts and shuts down when it warms up. See the top left and bottom right capacitors both with burst tops.
View attachment 168173
It's always possible Scott but normally you can spot them. I have had them where you can't tell but the replacement fixed it.
This is the 15", took a couple shots. If you want I can strip the case of tonight to show you the guts.