cffile copy / cfcontent download & delete

I am using CFFILE to copy a file to a TEMP location and then using CFHEADER and CFCONTENT (with deleteFile set to "yes") to start a download of a file (from the TEMP location) and delete it when download finishes (or is aborted). My question is this: what will happen if multiple requests are made simultaneously for the same file? Is this gonna be a problem? If so, what's the workaround (if any)?