Hi.
The problem with your computer is of hardware origin. Presently you identified two problems which may, or may not be related:
1) BSODs
2) CPU ovgerheating.
BSODs are commonly (but not exclusively) caused by faulty hardware. It may be the RAM, CPU, motherboard, unstable PSU etc. An overheating CPU is an unstable one and can easily cause the same problems. It's very possible that a RAM module is defective but the fact that you got a number of memtest runs showing no problem but then you got bad results look suspicious to me. To pinpoint the problem we must diagnose it systematically.
I suggest the following:
1) Since you already ordered new RAM modules, please install them. You shouldn't worry, they will not be damaged. With some luck that will solve the BSODs problem.
2) To find if you have another graphic card in your computer (a one which is integrated into the motherboard) look at the back of the computer and see if you have another connector for which the monitor cable can be connected. If you do have one, please take the overheating one out and connect the monitor to the buit-in one and see if it makes any difference. It is very possible that your computer does not have another graphic card.
3) Regarding the overheating: We looked for obvious causes such as faulty fans, blocked air inlets etc. There are other possible causes such as faulty PSU or CPU. Having admitted your limited knowledge in computer repair (which is the case with most posters to this forums), you may be better off taking the computer to a decent technician who has the knowledge and means to diagnose and solve the problem.
Kind Regards / The Skeptic