I'm new to this, so you might have to bear with me. I want to try to help, though, as I am using the exact same computer (Dell XPS L502x) and installed Ubuntu 12.04 LTS last week. I miss the Waves MaxxAudio program, but I don't feel like I'm experiencing loss in audio quality with Ubuntu.
lspci -v | grep -A7 -i audio gives me the same output as you, except Subsystem: Dell Device 050e. I'm assuming one of us just has a sound device with minor differences, and I don't think this is related to your problem.
Have you looked at the information found at this link, specifically question 5? Piping the find command to wc -l gives me 220 results, what does yours return? Since the device is detected with lspci I'm not sure if this is the issue, but worth a check.
Can you paste (paste.ubuntu.com) the output of aplay -l and aplay -L?
Also, in Synaptic Package Manager, make sure you have libportaudio2, libaudio, libasound2, and libsndfile1 installed. If it's a particular type of file that you're playing make sure the proper codecs are installed.
Most likely the source of heat is not CPU, but video card. You notebook has 2 video cards, with the idea that slow but cool HD400 works by default, switching to hot and powerful one when needed. (which one do you have by the way? They vary in this model). In Linux, this does not work out of the box, and you always have both video cards on, resulting in maximum heat.
If you are OK to go without big GPU, you can just disable bigger video card altogether. Intel HD4000 is a rather tough guy itself - it can handle HD video and all 2010 games quite well. Otherwise, search for instruction on how to tweak NVIDIA Optimus if you have NVIDIA, or PowerXPress if you have Radeon. These are the names of technologies that use 2 video cards to save power.
Best Answer
I had the same problem. I solved it by installing Bumblebee.
It seems like it was a problem with power management. After installing Bumblebee and restarting my computer, it ran smoothly, with quiet fan and at normal temperature. Actually, now my battery last longer in Ubuntu than it does on Windows 7.