Has the laptop ever been cleaned? Sometimes it overheats because the fans are blocked. It could also be the thermal paste needs replacing.
I have an old MacBook Pro, it has overheating issues too. It gets to a constant 104C (219F), and will melt a chocolate chip cookie within 5 to 7 minutes.
I tried redoing the thermal paste and nothing changed, the fans are also fine. So is everything else. It could be that your device is somewhat like mine, it's randomly decided to rebel and become annoying to use.
Perhaps it could be the battery or the charging cable, I've only been fixing computers for 2 years now so I don't know ''too'' much, but seeing as this is simular to mine, I thought I may suggest the things that I tried when I had this issue.
Good luck, and don't use it on your lap without something between it and your legs. :)