Magento – How to send set password email

1. Store the IP address and/or user agent used when the customer last placed an order or visited and make the link only work with that IP address or user agent.
2. Make the link only work one time.
3. Require some really easy intermediate authentication like "To confirm you are Jane Doe, please enter your zip code:"

You didn't specify a Magento version so I'll explain it based on the current version CE 1.9.1.0. If you are sure that sendNewAccountEmail() isn't used I'd suggest you have a look at sendPasswordReminderEmail() in app/code/core/Mage/Customer/Model/Customer.php.

Here is an explanation:

• When you submit the customer submit form, the method Mage_Adminhtml_CustomerController::saveAction() is triggered.

• The password and e-mail logic starts in the code block around line 305:

  $isNewCustomer = $customer->isObjectNew();
  try {
      $sendPassToEmail = false;
      // Force new customer confirmation
      if ($isNewCustomer) {
          $customer->setPassword($data['account']['password']);
          $customer->setForceConfirmed(true);
          if ($customer->getPassword() == 'auto') {
              $sendPassToEmail = true;
              $customer->setPassword($customer->generatePassword());
          }
      }
      Mage::dispatchEvent('adminhtml_customer_prepare_save', array(
          'customer'  => $customer,
          'request'   => $this->getRequest()
      ));
  
      $customer->save();
      // ...
  } // ...
  

  Here, the password for a new customer would be generated.

• Next, the mails are sent:

  // Send welcome email
  if ($customer->getWebsiteId() && (isset($data['account']['sendemail']) || $sendPassToEmail)) {
      $storeId = $customer->getSendemailStoreId();
      if ($isNewCustomer) {
          $customer->sendNewAccountEmail('registered', '', $storeId);
      } elseif ((!$customer->getConfirmation())) {
          // Confirm not confirmed customer
          $customer->sendNewAccountEmail('confirmed', '', $storeId);
      }
  }
  if (!empty($data['account']['new_password'])) {
      $newPassword = $data['account']['new_password'];
      if ($newPassword == 'auto') {
          $newPassword = $customer->generatePassword();
      }
      $customer->changePassword($newPassword);
      $customer->sendPasswordReminderEmail();
  }
  

  Normally, the mail template customer_create_account_email_template is used when a new user registered and confirmation is not required (i.e. $customer->sendNewAccountEmail('registered', '', $storeId); in the snippet above).

  As you imported the customer before and just re-save it with a auto-generated password, the second part of the code should apply and the mail should be sent here:

  $customer->changePassword($newPassword);
  $customer->sendPasswordReminderEmail();
  

  This method sendPasswordReminderEmail() which can be found in app/code/core/Mage/Customer/Model/Customer.php uses the mail template configured as the "Remind E-Mail Template".