Check out :
http://search.cpan.org/~autrijus/PAR-0.85_01/script/pp
And the option:
-L, --log=FILE Log the output of packaging to a file rather than to stdout.

Or if you need to use STDOUT for something else (doesn't sound like it), you can make your own logfile and redirect warnigns/errors to it

# make sure errors are put into the logfile
    # i.e. print STDERR "weird" ~ not in logfile
    #         warn "freaky"        ~ in logfile (and the screen)
    #        die "AAaaarrrrrgh!" ~ in logfile
    $SIG{__WARN__} = sub {print $log_file @_;print STDOUT @_};
    $SIG{__DIE__} = sub {print $log_file @_;print STDOUT @_;exit 1};
[download]

Or use Log4Perl or Log::Handler to more or less the same effect.
Hope this helps.