You could try and see what mail format is used by Evolution. Chances are that this format is the mbox one (several mails in a file, one file per "mail folder") at the heart of it, even though Evolution would add metadata files alongside. You should be able to copy those mbox files to the "Local Folders" of Thunderbird.
In the worst case, you can easily setup a local IMAP server, copy all mails to this server using Evolution, and get them all from the server using Thunderbird.
Myself, I use an IMAP server (BincImap) all the times, so I can change of mail client at will