Hey OG, don't despair and throw away that baby just yet! Just because there are new packages literally every day does not mean you have to frantically upgrade! I sure don't. Klaus and other live CD's maintainers are doing a wonderful job of periodically giving us a nice snapshot of the state of the art in linux, so just enjoy their creation.

Back to your original question, installing a .tar.gz package can be done under debian, of course. It just bypasses the normal procedures and apt won't have a clue about this particular SW. The .tar.gz extension indicates a "compressed tar archive", with tar being an old trusty unix archiver. It could contain either source code or binary executable. In the first case, you usually need to do "configure; make; make install", but it may fail due to unmet source libraries dependencies. This is exactly what apt handles for you, by just tapping into repositories of compiled binary packages, with automatic dependency management. The second case - and following the default thunderbird link for linux seems to provide that kind of binary - just needs to be unpacked. Generally under the top-level directory you'll find an executable, eg: thunderbird-X.Y.Z/thunderbird.

Now I know it all can seem overwhelming or downright scary at first. Let me then remind you that you can simply use mozilla mail, as I do! If your knoppix is reasonably recent and has mozilla 1.5 or better, it'll have all thunderbird has to offer, eg decent client-side spam filtering and spell checking.