Very easy method, replace existing code in /system/library/cart
$this->db->query("DELETE FROM " . DB_PREFIX . "cart WHERE (api_id > '0' OR customer_id = '0') AND date_added < DATE_SUB(NOW(), INTERVAL 1 HOUR)");
New Code
$this->db->query("DELETE FROM " . DB_PREFIX . "cart WHERE date_added < DATE_SUB(NOW(), INTERVAL 1 HOUR)");