Re: Dell XPS L501X shutting down randomly
Don't worry about the diagnostic partition, it's not present because you've done a clean install of Windows.
Good news about the lower temps. Clean the vents from time to time and consider using the laptop with a laptop cooler pad which may reduce temps further.
Regarding the blue screens. This could be just a case of keeping your systems drivers up to date. Visit Dell support website for updated drivers and bios updates.
Hopefully you shouldn't experience anymore random shutdowns, but if you do then post back for more assistance.