With for sure ruling out the temperature issue, it could be quite a bit of things. The things I would probably check for first are:
- The power supply. It could be going bad.
- Some part of the power cord/battery is having issues.
- Memory is going bad.
- Motherboard Issues
- Infected with a virus
Considering it's a laptop, I wouldn't necessarily advise you to open it up and reference some links on the web on what you'd need to do. Because that would just be asking for a disaster. I would however, go with tackling my last bullet there. Install Malwarebyte's program, and run it. Additionally, run a virus scan. This being a software route of troubleshooting is at least a start. If there is no improvements after doing that, I'd suggest having someone comfortable with laptops and their hardware take a look at the aforementioned bullet list, or take it to a repair place. All and all, if its the power supply, it could run him up to ~100$. The cord/battery will vary in price, but probably less than the power supply. Memory is going to be a bit more than the power supply, and the mobo is going to be a huge price range.
Hope this gives you some direction