Why not fork a separate process from your script to handle it? Something like this (untested):

END {
    my $pid;
    if ($pid = fork){
        exit;
    }elsif (defined $pid){
        close STDOUT; 
        sleep 5;
        unlink ($tempfile);
    }else{
        # if fork fails:
        sleep 5;
        unlink ($tempfile);
    }
}
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