Ubuntu still comes with a version of Linux that has certain firmware inside.
Even if you use the open-source drivers in Ubuntu, it means that you are
using the non-free firmware that is included in the kernel itself. That is of
course missing in Trisquel. That reveals how some of the supposedly
open-source drivers aren't so open-source after all.
I can't find any specific information about the hd4330, but I don't see
reports on any hd4xxx being more or less fully reverse engineered. I'm afraid
that the only way to prevent overheating your stuff is to use the proprietary
driver (or Ubuntu, it has the firmware anyway).
The perfect solution would be to buy a laptop from a manufacturer who isn't
lobbying for some operating system. ThinkPenguin has some really cool ones
(don't be fooled by the low quality pictures there, the laptops look very
good in real life as reviews have shown). Your favourite searchengine will
find you a review of the PenguinAir, afaik it's the only review of a
ThinkPenguin laptop so far.