Lightroom :: 5 Taking Up Local Disk Space While Publishing?

I have a relatively large photo catalog (200k photos +) that I am in the process of paring down with Lightroom 5.  Along the way I have kept certain groups of photos published to Flickr using Smart Photosets so that if I eliminate a duplicate photo from the catalog I will be able to "re-publish" and eliminate that duplicate from the published collection.
 
My Catalog Files, My Backups, and the actual image files that are referenced in the catalog are all located on an external drive.  I did this so that I could have everything on one drive for the time being while I eliminate a ton of photos from the catalog.
 
The issue that I am running into is that while a collection is being published to Flickr I get a message popping up telling me that I am low on disk space on my local (C) drive and that I need to free up some space.  This is odd because everything is located on the external drive (catalog and image files) and I am publishing to Flickr.
 
I am just trying to figure out if there is a default somewhere that is causing Lightroom to create new thumbnails or previews somewhere on my C drive while I am publishing images to Flickr or something like that.  What sort of data might be accumulating in the process here?  And is there anyway to move it all or eliminate it for the time being while I am finishing the elimination of duplicate files from my catalog?