Preparing Your Thunderbird
Create a new mail account in Thunderbird (this is so that if everything goes pear shaped nothing else will be affected).
In Thunderbird choose Edit -> Account Settings -> Add Account
Select Email Account and click Next
Leave identity settings as they are and click next
Set the Incoming Server to "localhost" and REMOVE the tick from "Use Global Inbox" Click next
Leave the Incoming user name as it is. Click Next
Change the Account Name to something relevant such as "Evolution Mail"
Once the settings are created return to Edit -> Account Settings and select the "Server Settings" option under the "Evolution Mail" account. Take note of the "Local Directory" Setting. It will be a string like "/home/yourloginname/.mozilla-thunderbird/a2ti6rsz.default/Mail/localhost". This is where all mail is stored for this account.
Now that the account is created and you know where to find it you can transfer the emails from Evolution.
Transferring mail from Evolution to Thunderbird
Open up two windows to your Home Directory. Navigate in one of the windows to the path that Thunderbird has assigned for your email storage above. HINT: CTRL+h in your home folder will show all hidden files and folders so you will be able to see the ".mozilla-thunderbird" folder. Once you are in this folder you will see some files in there with names such as Inbox, Inbox.msf, Junk.msf and so on.
In the other window from your home folder navigate to ".evolution/mail/local" This is where any locally stored mail from Evolution is placed. There are a similar set of files to what you see in the Thunderbird folder, Inbox, Drafts and so on.
Copy the files named Inbox, Sent, Outbox and Drafts from the evolution folder to the mozilla-thunderbird folder (dragging and dropping while holding down your ctrl key will copy rather than move the files). When it asks if its ok to overwrite them just say yes. Its ok, nothing bad will happen. Its just a copy. You can trust me. Honest.
If you have your mail folders organised in evolution under your Inbox there will be a sub directory called "Inbox.sbd" under the .evolution/mail/local/ directory. In that directory you will find files named the same as your folders such as Humour, Humour.cmeta, Humour.ev-summary, Humour.ibex.index and so on. Of course, this depends on what you've called your folders.
For any of the folders you want to move to Thunderbird chose the file WITHOUT any extension and copy it to the localhost folder where you previously placed the Inbox and other files.
Thats all there is to it! Open Thunderbird and you should see all your mail and the relevant folders under the "Evolution Mail" account. You can keep the mail there or move it around in Thunderbird. The choices are yours.