You can upgrade Thunderbird to version 12 beta that is available in the Mozilla team PPA.

To install Thunderbird 12, run the following commands in the terminal:

sudo add-apt-repository ppa:mozillateam/thunderbird-next && sudo apt-get update

sudo apt-get install thunderbird

After the first two commands you will see the text:

You are about to add the following PPA to your system:
 Official PPA for Thunderbird Beta
 This PPA contains releases of Thunderbird from the beta channel

All users of this PPA are encouraged to report any bugs they find. Instructions for reporting bugs can be found at https://wiki.ubuntu.com/MozillaTeam/Bugs. Please have a read of this before reporting a bug, as it may help save time
 More info: https://launchpad.net/~mozillateam/+archive/thunderbird-next

You can start using Thunderbird 12 beta by launching it from the Mint menu.

You can find it in the "Internet" category under the name "Thunderbird Mail", as it replaces your previous installed stable version.

You can also install Thunderbird 15 alpha that is available in the Mozilla daily PPA.

To install Thunderbird 15, run the following commands in the terminal:

sudo add-apt-repository ppa:ubuntu-mozilla-daily/ppa && sudo apt-get update 

sudo apt-get install thunderbird-trunk

After the first two commands you will see the text:

You are about to add the following PPA to your system:
 Firefox and Thunderbird daily builds
 daily (or even multiple builds per day) for various mozilla projects and branches.

For questions and bugs with software in this archive, please contact <email address hidden> or visit #ubuntu-mozillateam on freenode.
 More info: https://launchpad.net/~ubuntu-mozilla-daily/+archive/ppa

Please note that the name thunderbird-trunk is used instead of thunderbird as it will be installed as "Nightly Thunderbird Mail".

You can start using Thunderbird 15 alpha by launching it from Terminal with the command

thunderbird-trunk

It should work at the same time with your current stable or beta version.