I am a 100% sure if you delete all the files that have a .tmp extension, it won't mess anything up.
42 tmp files is VERY low for 2 years of usage.
Do you have your browser set to delte all offline and temporary files when closing?
You probably won't be able to delete EVERY file in that view, but delete as much as possible.
If you are a little nervous about performing this action, you can change the view of the search results to "Description" and it will show you the size of each individual temp file. If you find a big one, just delete that one.