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{
    "new_version":"1.0.1",
    "url":"http:\/\/domain.com\/theme\/theme\/",
    "package":"http:\/\/domain.com\/theme\/theme\/mco.zip"
}

<?php
/**
 * Add theme updating functionality
 */

 function theme_pre_set_transient_update_theme ( $transient ) {
  if( empty( $transient->checked['theme_name'] ) )
     return $transient;

   $ch = curl_init();

   curl_setopt($ch, CURLOPT_URL, 'http://domain.com/theme/theme.json' );

  // 3 second timeout to avoid issue on the server
  curl_setopt($ch, CURLOPT_TIMEOUT, 3 );
  curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);

  $result = curl_exec($ch);
  curl_close($ch);

  // make sure that we received the data in the response is not empty
  if( empty( $result ) )
    return $transient;

  //check server version against current installed version
  if( $data = json_decode( $result ) ){
    if( version_compare( $transient->checked['theme_name'], $data->new_version, '<' ) )
  $transient->response['theme_name'] = (array) $data;
  }

  return $transient;

 }
 add_filter ( 'pre_set_site_transient_update_themes', 'theme_pre_set_transient_update_theme' );