If it helps at all, you can tell CGI.pm to use a specific directory for its temp files like this:

$CGITempFile::TMPDIRECTORY = $myTempDir;
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That way you could put them in your own directory and delete them yourself without bothering your admin. I think it will work as long as you just include that line before you create a CGI object, but maybe you need to put it in a BEGIN block.

If you're still using an older version of CGI.pm, the package name may be different, like this:

$TempFile::TMPDIRECTORY = $myTempDir;
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