Well, it sounds to me as though you HAVE got it fixed! Overheating, though, may be caused by a build up of dust around the heat sink that the fan blows through. This can be a bit tricky to deal with on a laptop without a lot of dismantling. Viruses can leave a lot of problems behind (such as the flashing cursor/black screen). I would do a deep scan with the free version of Malwarebytes and also run CCleaner.
The best way to clear the dust is to blow compressed air into the air outlet, but put a paperclip or similar through the air inlet to stop the fan spinning when you do that (the fan motor can act as a generator and screw up the mobo).