In order to add the file to the email as an attachment, it will need to be stored on the server briefly. It's trivial, though, to place it in a tmp location then delete it after you're done with it.
As for emailing, Zend Mail has a very easy to use interface for dealing with email attachments. We run with the whole Zend Framework installed, but I'm pretty sure you could just install the Zend_Mail library without needing any other modules for dependencies.
With Zend_Mail, sending an email with an attachment is as simple as:
$mail = new Zend_Mail();
$mail->setSubject("My Email with Attachment");
$mail->addTo("[email protected]");
$mail->setBodyText("Look at the attachment");
$attachment = $mail->createAttachment(file_get_contents('/path/to/file'));
$mail->send();
If you're looking for a one-file-package to do the whole form/email/attachment thing, I haven't seen one. But the individual components are certainly available and easy to assemble. Trickiest thing of the whole bunch is the email attachment, which the above recommendation makes very simple.