Hi, Major Paul. Premiere Elements has its own forum and you'll get better help with PRE if you ask there. I'll move this for you.
Yes, do remember that the program is also saving work files to wherever your Premiere Elements project file is located (which, by default is in your Documents folder on your C drive).
The best advice is, whenever start a new project, is to save it in a new, separate folder on our D drive. This will keep all of the project's supporting files on your D drive -- where you apparently have lots of space.
Meantime, do keep your C drive as clean as possible. The larger percentage of your C drive that you keep clean and empty (run Disk Cleanup regularly), the more stable your system will run. I'm concerned that your C drive seems to be filling up. Once its free space gets between 30 gigs, you'll start to experience problems. So follow my advice and keep your project files on your D drive-- ideally each project in its own folder -- and things should work much better.
Welcome to the forum.
I agree with Steve 100%. Much of what you are likely seeing on your C:\ are the Scratch Disks for Premiere, which are "working files." One has the option of where to locate those, in Edit>Preferences, and if you take Steve's advice of creating your Projects on your D:\ to begin with, then I would adjust the destination of all of the Scratch Disks to "Same as Project," and they will then reside on D:\, below the Project's folder in the hierarchy.
Also, there is a recent thread on Scratch Disks (though the discussion does include Photoshop's Scratch Disks, which are different) here: http://forums.adobe.com/thread/1156141?tstart=0
As Steve also suggests, keeping one's C:\ as clean, as is possible is a very good thing, and I could not agree more.