As you said, sounds like you might have a hardware issue around cooling… 
Laptops are difficult to cool and quality varies.
I have an ASUS ROG laptop an have been quite happy with it - the newer ones have full-blown gtx 1070 which is basically a desktop chip (latest nvidia line does not have separate chips for mobile anymore because of the lower power requirements).
I have also heard good things about the new Razer with the 1060 in it.
Maybe try to sell your old one and get a new one?