Oh oh Elwyn does your graphics card have a control center on the pc anywhere? where you can enable/disable certain things for it? and where you can slide down the rendering? (it will make the game models look like clay and a bit jagged~ but helps!)

I have an acer laptop I use for wandering around the house. Was able to play Divinity on it, but I had to turn everything in game and on the graphics card to the bare minimum. Things looked really blurry n sorta odd~ but it played!

Heating issue! I am not sure if I missed it while reading (sorry if I did) but do you have a cooling stand? I have an old one I use. It pretty much just holds the laptop at a slight angle so there is airflow.
Here is a picture of one of the newer models with a fan in it o.o (might need to upgrade mine =p)

[Linked Image]

Has Divinity been optimized yet? maybe you could suggest a laptop compatibility graphics setting.