Is your music stored on your computer or are you streaming it live? If streaming, it could be download amount controls.
Does your music play with film (video) and not just music? If with film you can, to make it a little lighter to run, convert the video to music only with VLC or YTD.
Have you tried to play your music with another player? This will let you know if it is only WMP. Try VLC, etc. [as stated in cokedude's answer]. You should find the Event Reports (in Admin tools) for this as they could provide a error ID from which you can refine the search for a solution.
Does your fan make noise and over heat while doing anything other - say watching a film? Turning itself off is on the serious side and you should check the fan and CPU.
Putting all this aside, it could be that you have copied the music one to many times and it has missed some bits. If this is a possibility, try and find an older backed up version and see how the new copy works (this is what happened to me and how I fixed it).