I did a huge technological jump from R600 to P50 lately. Not that I love the P50, it just gives the kick I need

The problem is, it does behave... well, weird.
First of all, the system hibernates out of nowhere when under load. This does not seem to be connected with temps, as they are kept in lower 80s. System has been dusted and repased couple of days back. I did not check if the problem occurs with no battery installed, and I think the battery might be a good track. At first I was putting the blame on A/C adapter, but 20,4V it gives is still within limits.
Second thing are the temps - I did some synthetic tests, and they vary deeply between software used. Prime95 could easily produce 95C on CPU, and the clock drops to 2,8GHz staying there during the test, and Orthos test does not exceed 85C with clock fluctuating etween 3,1 and 3,3GHz.
The last thing is the cursor that... just goes off time to time. It simply disappears or stops responding. I did not check it on external mouse though, so this may be a synaptics driver problem.
I'd be grateful for you suggestion, especially with the "hibernate" problem. Maybe I'm looking wrong way and it's completely not in there.