Although overkill for the example you showed, it might be useful to see how this can be done with SQL. The following uses DBD::CSV so it can work with your input files directly to produce your expected output, though for "production" work you would probably want to use a real database. Also, my output code is somewhat simplistic, one could use Text::CSV(_XS) for that purpose as well.

use warnings;
use strict;
use DBI;

my $dbh = DBI->connect("dbi:CSV:", undef, undef, {
        csv_sep_char => "\t", f_ext => '', RaiseError => 1,
    }) or die "Cannot connect: $DBI::errstr";
 
my $sth = $dbh->prepare(<<'ENDSQL');
SELECT
    tmp01.PeptideID as PeptideID,
    tmp01.ProteinID as ProteinID,
    tmp02.SpectrumID as SpectrumID,
    tmp02.Sequence as Sequence
    FROM tmp01
    LEFT OUTER JOIN tmp02
        ON tmp01.PeptideID = tmp02.PeptideID
ENDSQL
$sth->execute;
print join("\t", @{ $sth->{NAME} } ), "\n";
while ( my $row = $sth->fetchrow_arrayref ) {
    print join("\t", @$row ), "\n";
}
[download]

Update: Also make sure to read up on the different kinds of SQL JOINs to see the difference between those and which one is appropriate for your case.