I had this problem on my Gentoo boxes where you click on a link sent in an email and it opens nothing. This is similar to a reverse problem of opening mailto links in Thunderbird found here. Just follow these directions and soon you will have your links opening in Firefox (or a different browser with a slight modification).
You will need to go into your Thunderbird profile to do this. In your home directory, you should have a hidden directory named .thunderbird. If you don't have that, you may have something similar like .mozilla-thunderbird. Open the .thunderbird directory.
In the .thunderbird directory, you should have something similar to this:
$ ls -l total 9 -rw-r--r-- 1 jdeiman jdeiman 335 Feb 27 12:06 appreg drwx------ 3 jdeiman jdeiman 160 Feb 27 15:00 eclipse drwx------ 6 jdeiman jdeiman 960 May 10 15:02 nnx9f70w.default -rw-r--r-- 1 jdeiman jdeiman 94 Feb 27 12:06 profiles.ini
Your default profile directory is the one entitled <some characters>.default. Open that directory.
Now, all that's left is to create a file called user.js and put the following lines in it (modify appropriately to reflect your path to the firefox binary):
user_pref("network.protocol-handler.app.http", "/usr/bin/firefox");
user_pref("network.protocol-handler.app.https", "/usr/bin/firefox");
Now, just restart Thunderbird and your links should open up in Firefox.