HTML5 WebSockets are only supported by IE10+; so you would not be able to use it in older versions of IE. And... you do not want to use temporary tables or memory tables; because you said you want to keep all these chat conversations in a permanent database. Storing these chats in a temporary/memory database / data table, would only store them for a limited amount of time (based which table storage method you implemented).
Thanks a lot. I see. Then I have to implement the permanent tables with a short polling AJAX (two ways) as I am doing now.