On your old system, run:
Then copy thunderbird_backup.tar.gz to a USB stick or whatever you're using to store your files during your reinstall.
tar czvf thunderbird_backup.tar.gz ~/.thunderbird
On your new system, drop it into your home folder and run:
The mv command is only necessary if you've opened thunderbird already on the new machine, since we don't want any new settings to interfere with the old profile.
mv .thunderbird thunderbird_old
tar xvf thunderbird_backup.tar.gz
When you next start thunderbird you should get all your old stuff just like nothing's changed.