Depends on where you are reading the info for the GPU and where you got the info saying you should have the other kind of GPU.
Also, you kind of stated why you would be having problems right in the info you gave. You said yourself that it is overheating. If that is the case, that could easily give you problems.
What you need to get it to stop overheating. This may just require cleaning out the inside of dust, debris, clearing fans and vents, etc. I could also mean you need to replace all thermal paste or even replace a fan or two. Hopefully you can get the temps down before damage can occur to the GPU or even the motherboard.
NOTE: If the laptop is under warranty, don't do any of this yourself or take it to a local person. In such a case you should contact the manufacturer about a repair.