How to use drupal_mail() to send emails with custom template
If you are trying to send the mails via your custom module then you can follow the below mentioned guide. 
Say, I had one Module called "Commerce Canvas(commerce_canvas)"
 1. First Alter the Drupal's mail function to support links and add other encoding types


/**
 * Implements hook_mail_alter()
 * @param string $message
 */
function commerce_canvas_mail_alter(&$message) {
    $headers = array(
        'MIME-Version' => '1.0',
        'Content-Type' => 'text/html; charset=iso-8859-1; format=flowed',
        'Content-Transfer-Encoding' => '8Bit',
        'X-Mailer' => 'Drupal',
    );
    foreach ($headers as $key => $value) {
        $message['headers'][$key] = $value;
    }
}



Then next, hook the HOOK_mail in your module as 




/**
 * Implements hook_mail()
 * @param string $key
 * @param string $message
 * @param unknown_type $params
 */
function commerce_canvas_mail($key, &$message, $params) {

    //Language Selection
    $options = array(
        'langcode' => $message['language']->language,
    );
    switch($key) {
        case "user_payment_notification" :
            $message['subject'] = isset($params['subject']) ? $params['subject'] : $message['subject'] = t('Payment recieved @site-name', array('@site-name' => variable_get('site_name', 'Express Canvas')), $options);
            $message['body'][] = isset($params['body']) ? $params['body'] : NULL;
            if (isset($params['headers']) && is_array($params['headers'])) {
                $message['headers'] += $params['headers'];
            }
            break;
    }
}





Then you need to create a wrapper function to invoke the mail from your module. 




function commerce_canvas_mail_send(array $values = array()) {
    $module = $values['module'];
    $key = $values['key'];
    $to = $values['to'];
    $from = $values['form'];
    $language = isset($values['lang']) ? $values['lang'] : language_default();
    $params = array(
        'subject' => $values['subject'],
        'body' => $values['body'],
    );
    if(array_key_exists('headers', $values)) {
        $params['headers'] = $values['headers']; //Assumed as an array
    }
    $send = TRUE;
    $mail = drupal_mail($module, $key, $to, $language, $params, $from, $send);
    if($mail['result']) {
        return TRUE;
    } else {
        $error_msg = 'Failed to send the email in commerce_canvas Module';
        watchdog('canvas-email', $error_msg, array(), WATCHDOG_ALERT);
        return FALSE;
    }
}



This function will send the email and as well as create debug messages if anything happens wrong.
But still you won't be able to send the HTML mail because you need to extend the Drupal 7's default DefaultMailSystem with your own. So need to do as following, 



class CommerceCanvasMailSystem extends DefaultMailSystem {
    /**
     * Concatenate and wrap the e-mail body for plain-text mails.
     *
     * @param $message
     *   A message array, as described in hook_mail_alter().
     *
     * @return
     *   The formatted $message.
     */
    public function format(array $message) {
        $message['body'] = implode("\n\n", $message['body']);
        return $message;
    }

    /**
     * Send an e-mail message, using Drupal variables and default settings.
     *
     * @see http://php.net/manual/en/function.mail.php
        * @see drupal_mail()
     *
     * @param $message
     *   A message array, as described in hook_mail_alter().
     * @return
     *   TRUE if the mail was successfully accepted, otherwise FALSE.
     */
    public function mail(array $message) {
        $mimeheaders = array();
        foreach ($message['headers'] as $name => $value) {
            $mimeheaders[] = $name . ': ' . mime_header_encode($value);
        }
        $line_endings = variable_get('mail_line_endings', MAIL_LINE_ENDINGS);
        return mail(
        $message['to'],
        mime_header_encode($message['subject']),
        // Note: e-mail uses CRLF for line-endings. PHP's API requires LF
        // on Unix and CRLF on Windows. Drupal automatically guesses the
        // line-ending format appropriate for your system. If you need to
        // override this, adjust $conf['mail_line_endings'] in settings.php.
        preg_replace('@\r?\n@', $line_endings, $message['body']),
        // For headers, PHP's API suggests that we use CRLF normally,
        // but some MTAs incorrectly replace LF with CRLF. See #234403.
        join("\n", $mimeheaders)
        );
    }
}




Next you need to register a new theme function that will call your custom template file in your hook_theme().



/**
 * Implements hook_theme();
 */
function commerce_canvas_theme($existing, $type, $theme, $path) {
  if($type == 'module') {
    return array(
      'tracking_code_email' => array(
        'variables' => array(
          'image_path' => NULL,
          'user' => NULL,
          'page' => NULL,
        ),
        'template' => 'commerce-canvas-tracking-code',
        'path' => drupal_get_path('module', 'commerce_canvas').'/theme',
      ),

    );
  }
}



Last you need to call this theme function in time of sending the email as, 




function a_custom_function($params) {

$email_text_user = theme('tracking_code_email', array(
                    'image_path' => $base_url . '/' . drupal_get_path('module', 'commerce_canvas') . '/images',
                    'user' => null,
                    'page' => array(
                        'greet_text' => t('Thank you for your order at Express Canvas. Your order is ready and has shipped. You may track your order using FedEx tracking with your tracking number: '.$order->field_tracking_number['und']['0']['value'].''),

                    ),
                ));
$sent_to_user = commerce_canvas_mail_send($email_values_user);

}



These are the full snippet to handle the HTML email correctly in Drupal 7 thus in the hook_theme you can give your custom template.