How to add variables to a template

I am using a query argument detail to check if a custom template should be loaded. This works fine, but I also need to add some variables that can be accessed from within the template. Here I am using add_action('template_include' array($this, 'templateInclude'):

public function templateInclude($template)
{
    if (get_query_var('detail', false) !== false) {
        // Check theme directory first.
        $newTemplate = locate_template(array('detail.php'));
        if ($newTemplate != '')
            return $newTemplate;

        // Check plugin directory next.
        $newTemplate = plugin_dir_path(__FILE__) . 'templates/detail.php';
        if (file_exists($newTemplate)) {
            return $newTemplate;
        }
    }

    // Return default template.
    return $template;
}

The above works, but of course I am not able to actually set any variables for the template.

I tried using set_query_var() to set a variable that could be accessed using get_query_var(), but this does not really seem to be the best solution.

I also tried using add_action('template_redirect' array($this, 'templateRedirect'), which works but this neither seems to be a really good solution:

public function templateRedirect() {
    if (get_query_var('detail')) {
        $detailId = get_query_var('detail', null);
        // Set a variable 'data' that can be used inside the template
        $data = get_detail($detailId);
        include plugin_dir_path(__FILE__) . 'templates/detail.php';
        exit;
    }
}

Would be really great if someone has some nice way of adding custom variables for a specific template.