I like the humor! I laughed!

Welcome wolvensun --Oops, I mean wolvenmoon.
You seem to already have some good electronic knowledge (well to non-electronicians). I am not an electronic guy but I do like these little silicon beasts.
Hot Glue is -- not good for overheating situations obviously(!)

For the cooling, ...well... you have been doing PC modding -- if there is an area where there is cooling involved, its PC modding! You even got to the point of getting your hands onto an expensive "laser" temp meter. So just put one of those super-duper-ultra-quiet-noctuaPaps-fan (that is probably around in your room?) to blow the heat out, or stick a huge CPU heat sink on it (another part lying in the room in a corner and screaming to do something else than stupidly collect dust). I would say try without a fan to see if it's enough (zero-noise), then add the fan if not enough. But overheating like that is .. not normal and unless you really cool it down (like shooting "freeze spray can" on the chip continuously) something is obviously dying or not right.
BTW, have you looked for "cold" solders (bad soldering)? Carefully inspect all the board pads and move the parts -- (especially through-holes ones). A bad solder could be the cause of overheating.
If you could post the picture of the spot that you think is the source of overheating -- which board is it?
Another option (depending where the fault piece is) would be to replace half of the circuitry by a monitor kit/LVDS controller. Essentially only keep the LCD Panel Component (and backlight). This type of operation is something people do everyday here. (well, not exactly everyday, but still, quite often).