I've never used it, but in my understanding Net::SMTP is a bit too low-level to have an explicit handling of the timestamp. From one of the examples

    #!/usr/local/bin/perl -w

    use Net::SMTP;

    $smtp = Net::SMTP->new('mailhost');

    $smtp->mail($ENV{USER});
    $smtp->to('postmaster');

    $smtp->data();
    $smtp->datasend("To: postmaster\n");
    $smtp->datasend("\n");
    $smtp->datasend("A simple test message\n");
    $smtp->dataend();

    $smtp->quit;
[download]

    #!/usr/local/bin/perl -w

    use Net::SMTP;

    $smtp = Net::SMTP->new('mailhost');

    $smtp->mail($ENV{USER});
    $smtp->to('postmaster');

    $smtp->data();
    $smtp->datasend("To: postmaster\n");
    $smtp->datasend("Date: Mon, 5 Jul 2004 11:35:36 +0200 (MEST)\n");
    $smtp->datasend("\n");
    $smtp->datasend("A simple test message\n");
    $smtp->dataend();

    $smtp->quit;
[download]

OTOH, if you're not telling the whole story and you're using some other module to build up your e-mail, like something in the MIME namespace, you probably have to look there for a way of setting the message date.

I would say this kind of work should be made by some other module. Searching CPAN for 'timezone' gives more than one result, as always. Your solution is probably in one of them.