@jamesm44572 first take care of the overheating issue. Use the [document|35663] to work on it. Start by opening it up and cleaning it out. Make sure that you clean the air vents. Next check and clean the fan. If you feel that the fan might be worn, consider replacing it. It is fairly inexpensive but vital to your computer.
The next thing you will have to do, is to replace the thermal paste between the heatsink and the processor. You already have had thermal shutdowns, you are most likely baking the paste as well. Time to replace it. Use this generic guide [guide|744] to replace it.
With everything cleaned, fan in working order and air vent clean, you are pretty much done with that. While you have the bottom cover open, just to a quick inspection of the display connector. Make sure that the LCD is connected and that there is no corrosion or any damaged looking component.
Now, it's time to figure out what is going on with your display. Since you board has already overheated it is always possible that his is related to a failed GPU. Do this. Connect an external monitor to your computer. If the external monitor shows your desktop etc. then you know the issues are with your LCD, display cable, display cable connector, or even the boost circuit on the motherboard.
If the external monitor doesn't show anything either the issue is most likely related to a bad GPU. That would require a board level repair or even a replacement motherboard.
Anyhow, let us know what you find out as you work on your computer. While you work on your phone, take lots of pictures. Once you are done with it, take those pictures and create a guide for iFixit. That will help the next person that has a device with the same issues as you do. It's easy and fun to create these guides. https://ifixit.com/Guide/new The iFixit community will appreciate this.
***Repair is War on Entropy!***