I work in a small office with about 35 people and we are all on a intranet. This network is not connected to the internet.

Is it possible to set up an email server, with which we could send emails to each other? (We don't need to send emails outside our network.)

I cannot use a messenger service like Openfire, since the messages could be asynchronous, and we'd like to get those emails in a email client like Thunderbird.

Another obstacle we have is that we do not have a domain name.

Any ideas on which free (as in beer) software could be used? We have both Windows and Linux machines.