You could easily install Thunderbird 3.1.x in Ubuntu using Ubuntuzilla, but that was only available for 32bit users.
A PPA repository is now available which provides the latest Thunderbird 3.1.6 (final, not daily builds) for Ubuntu Lucid - both 32bit and 64bit.
To add the PPA and install Thunderbird 3.1.6 in Ubuntu, simply paste the following commands in a terminal:
sudo add-apt-repository ppa:ricotz/ppa && sudo apt-get update sudo apt-get install thunderbird
Update: I've replaced the original PPA in this post with a new PPA which provides Thunderbird 3.1.6 packages for Ubuntu Maverick (10.10), Lucid (10.04), Karmic (9.10), Jaunty (9.04) and Hardy (8.04)!