Dear BHill,

 

You do not need take care the temp files.
Temp file means the uploaded data & info of a file. it's owned by uploader , not your application. 
Temporary files will be deleted after 5 hours (if the page load again after 5 hours). 

If you would like to remove temporary files once upload is finished, you can use the following code:

protected void attachment1_FileUploaded(object sender, UploaderEventArgs args)
    {
         //save upload file to another folder
         //you can change the upload file name here, like args.CopyTo("~/savefolder/"+"myname.jpg");
        args.CopyTo("~/savefolder/"+args.FileName);
         //delete the temporary files

        args.Delete();
    }