If you found the Ubuntuzilla way of installing Thunderbird 3.1 in Ubuntu a bit too hard, here is a .deb file you can download and install Thunderbird 3.1 in Ubuntu.
Note: this is the unmodified Mozilla release binary of Thunderbird, packaged into a .deb by the Ubuntuzilla project. This means they were only able to package it for 32bit since Mozilla does not provide 64bit binaries.
Many thanks to WebUpd8 reader eMcE for the tip!