Are you affected? The easiest way to check is look in the Error console Ctrl+Shift+J
The error message is quite distinctive and will take the form shown below;
What this means is that any server using SSL/TLS and 512bit encryption keys is not going to work with the updated Thunderbird. These keys have a long history. Introduced in the 1990's to meet US export restrictions on Cyphers. By the year 2000 these restrictions were lifted. But by that time the use of the so called Export Cypher suites was well entrenched.
Now 15 years on, when it was assumed basically no one would be using these obsolete suites, up pops a security vulnerability in them and we find that the "if it ain't broke don't fix it" approach to things is alive and well on the Internet. Here on the bleeding edge of technology, many large organisation, such as the NSA, are still using these obsolete and inherently insecure cypher suites.
There is a short term workaround for those using Thunderbird, by installing the add-on Disable DHE. This add-on is listed in the add-on site as for Firefox, but it will install in Thunderbird if you download it and drag it over the add-ons entries in the add-on tab. This is not a long term solution. You are still at risk of a man in the middle attack using it. But it gives breathing time to actually make arrangements for new key pairs to be generated for the server. You should contact the server administrator or your mail provider to make these arrangements.
I can not say it better than the team that found the vulnerability, so the following is extracted from their web site.
____________________________________________What should I do?
If you run a server…
If you have a web or mail server, you should disable support for export cipher suites and generate a unique 2048-bit Diffie-Hellman group. We have published a Guide to Deploying Diffie-Hellman for TLS with step-by-step instructions. If you use SSH, you should upgrade both your server and client installations to the most recent version of OpenSSH, which prefers Elliptic-Curve Diffie-Hellman Key Exchange.
If you use a browser…
Make sure you have the most recent version of your browser installed, and check for updates frequently. Google Chrome (including Android Browser), Mozilla Firefox, Microsoft Internet Explorer, and Apple Safari are all deploying fixes for the Logjam attack.
If you’re a sysadmin or developer …
Make sure any TLS libraries you use are up-to-date, that servers you maintain use 2048-bit or larger primes, and that clients you maintain reject Diffie-Hellman primes smaller than 1024-bit.