Theme Updater Example.

updater.php

<?php

if ( is_admin() ) {
	add_filter( 'pre_set_site_transient_update_themes', 'gb_check_for_premium_theme_update' );
}
function gb_check_for_premium_theme_update( $transient ) {
	$current_version = 1.2;
	$api_key = get_option('theme_api_key'); // your theme options will need to have an option to add the API key.
	$theme_slug = 'theme_slug'; // Change to match with API Key Manager
	$api_url = 'http://yoursite.com/check-key/'; // change to your site
	$basename = basename( get_template_directory() );
	
	// Get API response
	$theme_data_api = wp_remote_post( $api_url, array(
		'body' => array(
			'key' => $api_key,
			'plugin' => $theme_slug,
			'url' => site_url(),
			'wp_version' => get_bloginfo( 'version' ),
			'plugin_version' => $current_version
		),
		'user-agent' => 'WordPress/' . $wp_version . '; ' . home_url('/')
	) );
	$theme_data = json_decode( wp_remote_retrieve_body( $theme_data_api ) );
	if ( !is_wp_error( $theme_data_api ) && 200 == $theme_data_api['response']['code'] ) {
		if ( version_compare( $current_version, $theme_data->version, '<' ) ) {
			if ( version_compare( $current_version, $theme_data->version, '<' ) ) {
				$transient->response[$basename]['url'] = $theme_data->url;
				$transient->response[$basename]['slug'] = $basename;
				$transient->response[$basename]['package'] = $theme_data->download_url;
				$transient->response[$basename]['new_version'] = $theme_data->version;
			}
		}
	}
	return $transient;
}
// set_site_transient('update_themes', null); // uncomment for the updater to load everytime, used for testing