Implement contact form to print in the e-mail the taxonomy term name

Hello drupalers, long time I didn't open a new topic, because usually people had solved similar issues before me :)

I have a custom module which alter the core contact form. I read here and there and I was able to build a very simple module with hook_form_contact_site_alter.
then by hook_mail_alter I was able to implement the e-mail sent by the contact form.
Most part of my module came from a tutorial I found on a blog.

I have some custom fields, one of them is a select that call a vocabulary. "field_modello_macchina" is the taxonomy field reference. As first, I build the form

/**
 * Implements hook_form_FORM_ID_alter().
 */
function preventivo_form_contact_site_form_alter(&$form, &$form_state) {

$form['modello_macchina'] = array(
  '#type' => 'select',
  '#empty_option' => t('No specific machine'),
  '#title' => t('Machine Model Number'),
  '#options' => taxonomy_allowed_values(field_info_field('field_modello_macchina')),
  '#description' => t('You can select a Model to receive more information about a machine you are interested in')
);

this code renders the taxonomy term as desired.
Then I build the e-mail sent to the user.

/**
 * Implements hook_mail_alter().
 */
function preventivo_mail_alter(&$message) {
  if ($message['id'] == 'contact_page_mail'
    || $message['id'] == 'contact_page_copy') {
	$message['body'][] = t('Nome') .': '. $message['params']['name'];
    .....(other fields)....
	$message['body'][] = t('Modello macchina') .': '. $message['params']['modello_macchina'];
  }
}

The problem is: when I receive the e-mail it prints only the term id and not the human-readable term name.

Any suggestion on how to render the term name instead of tid?

Thank you very much for any help!