Thank you @ChrisUnderwood and @JoshuaBixby . None of those things happen on this server (site backups etc)
I went to Esri support with this question and was told the temp files are created when a process fails but that there is no way to tell what process created them. While it would be useful to know that, I was hoping to find an answer as to why these "temp" files are persisting for so long. It seems like they should be automatically cleaned up by either ArcGIS Server or Windows OS.
Apparantly that is not the case, though, and what we are seeing is expected behavior. So the lesson learned is to check your service account's appdata\local\ temp directory at least a few times per year and clean out the old stuff, or if your C drive suddenly fills up unexpectedly.
GISP