Similarly to the Firefox-Next PPA, there's a new "Thunderbird-Next" PPA available which you can use to install the latest Thunderbird beta builds in Ubuntu.
The Thunderbird Next PPA provides Thunderbird releases from the beta channel so each time a new beta version is released, it will be available to install via this PPA, but of course with a delay because it takes a while for new versions to be packaged and tested.
At the time I'm writing this post, the Thunderbird beta channel PPA provides Thunderbird 5 beta 1 - if you want to see what's new, see this page.
Upgrade To Thunderbird 5 beta 1 in Ubuntu using the Thunderbird beta channel PPA
Using this PPA, your current Thunderbird stable release will be replaced with the latest Thunderbird beta release, which may have bugs so use it at your own risk!
The Thunderbird Beta Channel PPA is available for Ubuntu 11.04, 10.10 and 10.04. Add it and upgrade Thunderbird to version 5 beta 1 using the commands below:
sudo add-apt-repository ppa:mozillateam/thunderbird-next sudo apt-get update sudo apt-get upgrade
P.s.: to get a Gmail-like interface for Thunderbird like in my screenshot, check out Thunderbird Conversations extension.